Stability of Weighted Norm Inequalities

We show that while individual Riesz transforms are two weight norm stable under biLipschitz change of variables on $A_{\infty}$ weights, they are two weight norm unstable under even rotational change of variables on doubling weights. More precisely, we show that individual Riesz transforms are unstable under a set of rotations having full measure, which includes rotations arbitrarily close to the identity. This provides an operator theoretic distinction between $A_{\infty}$ weights and doubling weights. More generally, all iterated Riesz transforms of odd order are rotationally unstable on pairs of doubling weights, thus demonstrating the need for characterizations of iterated Riesz transform inequalities using testing conditions for doubling measures, as opposed to the typically stable 'bump' conditions.Comment: 42 pages, followed by 9 pages of appendices and references. The proof of Lemma 30 is clarified with a modification of Lemma 28, a misprint in the proof of Lemma 30 (p.28) is corrected, the subsection of the appendix on the connection between A2 and biLipschitz maps is refined, and an additional subsection is added to the appendix relating stability and sparse operators. Main results unchange

Carleson measure estimates for caloric functions and parabolic uniformly rectifiable sets

Let $E \subset \mathbb R^{n+1}$ be a parabolic uniformly rectifiable set. We prove that every bounded solution $u$ to $$\partial_tu- \Delta u=0, \quad \text{in} \quad \mathbb R^{n+1}\setminus E$$ satisfies a Carleson measure estimate condition. An important technical novelty of our work is that we develop a corona domain approximation scheme for $E$ in terms of regular Lip(1/2,1) graph domains. This approximation scheme has an analogous elliptic version which is an improvement of the known results in that setting

Corona Decompositions for Parabolic Uniformly Rectifiable Sets

We prove that parabolic uniformly rectifiable sets admit (bilateral) corona decompositions with respect to regular Lip(1,1/2) graphs. Together with our previous work, this allows us to conclude that if $\Sigma\subset\mathbb{R}^{n+1}$ is parabolic Ahlfors-David regular, then the following statements are equivalent. (1) $\Sigma$ is parabolic uniformly rectifiable. (2) $\Sigma$ admits a corona decomposition with respect to regular Lip(1,1/2) graphs. (3) $\Sigma$ admits a bilateral corona decomposition with respect to regular Lip(1,1/2) graphs. (4) $\Sigma$ is big pieces squared of regular Lip(1,1/2) graphs.Comment: We have improved the exposition in section 4. In particular, we have treated the case where `contact set' in the Whitney-type construction is empty. This case seemed to be overlooked in David and Semmes' original construction, but only required a modest fix. We have also corrected the (egregious) typo in what is now equation (4.42), which now has $\epsilon$ rather than $\delta

Critical Perturbations for Second Order Elliptic Operators. Part I: Square function bounds for layer potentials

This is the first part of a series of two papers where we study perturbations of divergence form second order elliptic operators $-\mathop{\operatorname{div}} A \nabla$ by first and zero order terms, whose coefficients lie in critical spaces, via the method of layer potentials. In particular, we show that the $L^2$ well-posedness of the Dirichlet, Neumann and Regularity problems for complex Hermitian, block form, or constant-coefficient divergence form elliptic operators in the upper half-space are all stable under such perturbations. For instance, this allows us to claim the first results in the setting of an unbounded domain concerning the solvability of boundary value problems for the magnetic Schr\"odinger operator $-(\nabla-i{\bf a})^2+V$ when the magnetic potential ${\bf a}$ and the electric potential $V$ are accordingly small in the norm of a scale-invariant Lebesgue space. In the present paper, we establish $L^2$ control of the square function via a vector-valued $Tb$ theorem and abstract layer potentials, and use these square function bounds to obtain uniform slice bounds for solutions. The existence and uniqueness of solutions, as well as bounds for the non-tangential maximal operator, are considered in the upcoming paper.Comment: 73 page

Mineral Phosphate Solubilization in Burkholderia tropica Involves an Inducible PQQ-Glucose Dehydrogenase

Aims: The objective of this work was to provide knowledgement about the mechanism and regulation of the mineral phosphate solubilization in Burkholderia. tropica. To this end, the expression of the direct extracellular oxidative pathway in B. tropica was studied using different culture approaches.Study Design: Plate assays and batch cultures in flasks and bioreactor were carried out in this study with B. tropica Mto-293 like target organism. The experiments were achieved at least three times with two repetitions per time.Place and Duration of Study: Departamento de Química, Centro de Investigación y Desarrollo en Fermentaciones Industriales, UNLP, CCT-La Plata-CONICET, between November 2014-2015.Methodology: Qualitative plate assays with different Carbon sources were carried out for the evaluation of Mineral Phosphate Solubilization phenotype. Batch cultures in flasks were carried out with different Carbon, Phosphorus and Nitrogen sources to determine quantitatively soluble phosphorus, gluconic acid and other ketoacids in the supernatants, and also PQQ-linked glucose and gluconate dehydrogenase activities in whole cells. Cultures with some of the conditions mentioned before were carried out in bioreactor specifically to control pH.Results: This organism was able to produce significant amounts of gluconic acid via the expression of a PQQ-GDH and also showed a significant activity of GaDH. However, the direct oxidative pathway was only observed under conditions of Phosphorus starvation and/or Nitrogen fixation.Conclusion: The Mineral Phosphate Solubilization phenotype for B. tropica can be ascribed to the expression of the direct oxidative pathway which involves the expression of an active PQQ- linked glucose dehydrogenase. Nevertheless, this pathway is not expressed constitutively in this bacterium. Environmental conditions, like low P and N availability, led to an active extracellular glucose oxidation. Therefore, mineral phosphate solubilization in B. tropica involves an inducible pyrroloquinoline quinone-linked glucose dehydrogenase. These findings may contribute to the use of this bacterium as plant growth promoting bacteria reducing the dependence on chemical fertilizer.Centro de Investigación y Desarrollo en Fermentaciones Industriale

Mineral Phosphate Solubilization in Burkholderia tropica Involves an Inducible PQQ-Glucose Dehydrogenase

Aims: The objective of this work was to provide knowledgement about the mechanism and regulation of the mineral phosphate solubilization in Burkholderia. tropica. To this end, the expression of the direct extracellular oxidative pathway in B. tropica was studied using different culture approaches.Study Design: Plate assays and batch cultures in flasks and bioreactor were carried out in this study with B. tropica Mto-293 like target organism. The experiments were achieved at least three times with two repetitions per time.Place and Duration of Study: Departamento de Química, Centro de Investigación y Desarrollo en Fermentaciones Industriales, UNLP, CCT-La Plata-CONICET, between November 2014-2015.Methodology: Qualitative plate assays with different Carbon sources were carried out for the evaluation of Mineral Phosphate Solubilization phenotype. Batch cultures in flasks were carried out with different Carbon, Phosphorus and Nitrogen sources to determine quantitatively soluble phosphorus, gluconic acid and other ketoacids in the supernatants, and also PQQ-linked glucose and gluconate dehydrogenase activities in whole cells. Cultures with some of the conditions mentioned before were carried out in bioreactor specifically to control pH.Results: This organism was able to produce significant amounts of gluconic acid via the expression of a PQQ-GDH and also showed a significant activity of GaDH. However, the direct oxidative pathway was only observed under conditions of Phosphorus starvation and/or Nitrogen fixation.Conclusion: The Mineral Phosphate Solubilization phenotype for B. tropica can be ascribed to the expression of the direct oxidative pathway which involves the expression of an active PQQ- linked glucose dehydrogenase. Nevertheless, this pathway is not expressed constitutively in this bacterium. Environmental conditions, like low P and N availability, led to an active extracellular glucose oxidation. Therefore, mineral phosphate solubilization in B. tropica involves an inducible pyrroloquinoline quinone-linked glucose dehydrogenase. These findings may contribute to the use of this bacterium as plant growth promoting bacteria reducing the dependence on chemical fertilizer.Centro de Investigación y Desarrollo en Fermentaciones Industriale

Producing C-S-H gel by reaction between silica oligomers and portlandite: A promising approach to repair cementitious materials

Impregnation treatments are one of the alternatives to protect concrete-based building and monuments from weathering degradation. However, it is important to consider the chemical compatibility of the reaction products with the building material. The impregnation product studied here consists of a silica oligomer able to poly- merize, by a simple sol-gel process, inside the pore structure of concrete. In this work, we investigate the ability of this impregnation treatment to produce C-S-H gel in contact with cement paste. A complete characterization of the reaction products demonstrated that the silanol groups from silica oligomers react with the portlandite present in the cement paste generating a material with the chemical, structural and morphological features of C- S-H gel. Simultaneously, the 29Si NMR results indicate that the SieO units are incorporated into the existing C-S- H, increasing its chain length. These results open the way for a simple concrete structures repairing procedure. 1

Risk factors and outcome of COVID-19 in patients with hematological malignancies

Background: Prognostic factors of poor outcome in patients with hematological malignancies and COVID-19 are poorly defned. Patients and methods: This was a Spanish transplant group and cell therapy (GETH) multicenter retrospective observational study, which included a large cohort of blood cancer patients with laboratory-confrmed SARS-CoV-2 infection through PCR assays from March 1st 2020 to May 15th 2020. Results: We included 367 pediatric and adult patients with hematological malignancies, including recipients of autologous (ASCT) (n=58) or allogeneic stem cell transplantation (allo-SCT) (n=65) from 41 hospitals in Spain. Median age of patients was 64 years (range 1-93.8). Recipients of ASCT and allo-SCT showed lower mortality rates (17% and 18%, respectively) compared to non-SCT patients (31%) (p=0.02). Prognostic factors identifed for day 45 overall mortality (OM) by logistic regression multivariate analysis included age>70 years [odds ratio (OR) 2.1, 95% con‑ fdence interval (CI) 1.2-3.8, p=0.011]; uncontrolled hematological malignancy (OR 2.9, 95% CI 1.6-5.2, p20 mg/dL (OR 3.3, 95% CI 1.7-6.4, p<0.0001). In multivariate analysis of 216 patients with very severe COVID-19, treatment with azithromycin or low dose corticosteroids was associated with lower OM (OR 0.42, 95% CI 0.2-0.89 and OR 0.31, 95% CI 0.11-0.87, respectively, p=0.02) whereas the use of hidroxycloroquine did not show signifcant improvement in OM (OR 0.64, 95% CI 0.37-1.1, P=0.1). Conclusions: In most patients with hematological malignancies COVID-19 mortality was directly driven by older age, disease status, performance status, as well as by immune (neutropenia) parameters and level of infammation (high CRP). Use of azithromycin and low dose corticosteroids may be of value in very severe COVID-19