Small Hankel operators on generalized weighted Fock spaces

In this work we characterize the boundedness, compactness and membership in the Schatten class of small Hankel operators on generalized weighted Fock spaces $F^{p,\ell}_\alpha(\omega)$ associated to an $\mathcal{A}^\ell_p$ weight $\omega$, for $10$

Muckenhoupt type weights and Berezin formulas for Bergman spaces

By means of Muckenhoupt type conditions, we characterize the weights $\omega$ on \C such that the Bergman projection of F^{2,\ell}_{\alpha}=H(\C)\cap L^2(\C,e^{-\frac{\alpha}2|z|^{2\ell}}), $\alpha>0$, $\ell>1$, is bounded on L^p(\C,e^{-\frac{\alpha p}2|z|^{2\ell}}\omega(z)), for $1<p<\infty$. We also obtain explicit representation integral formulas for functions in the weighted Bergman spaces A^p(\omega)=H(\C)\cap L^p(\omega). Finally, we check the validity of the so called Sarason conjecture about the boundedness of products of certain Toeplitz operators on the spaces F^{p,\ell}_\alpha=H(\C)\cap L^p(\C,e^{-\frac{\alpha p}2|z|^{2\ell}})

Hankel Bilinear Forms on Generalized Fock-Sobolev Spaces on CnC^n

We characterize the boundedness of Hankel bilinear forms on a product of generalized Fock-Sobolev spaces on $\mathbf{C}^n$ with respect to the weight $(1+|z|)^p e^{-\frac{\rho}{2}|*|^{2 t}}$, for $\ell \geq 1, \alpha>0$ and $\rho \in \mathbf{R}$. We obtain a weak decomposition of the Bergman kernel with estimates and a LittlewoodPaley formula, which are key ingredients in the proof of our main results. As an application, we characterize the boundedness, compactness and the membership in the Schatten class of small Hankel operators on these spaces

Boundedness of the Bergman projection on generalized Fock-Sobolev spaces on C∧nC^{\wedge} n

In this paper we solve a problem posed by H. Bommier-Hato, M. Engli and E.H. Youssfi in [4] on the boundedness of the Bergmantype projections in generalized Fock spaces. It will be a consequence of two facts: a full description of the embeddings between generalized FockSobolev spaces and a complete characterization of the boundedness of the above Bergman type projections between weighted $L^p$-spaces related to generalized Fock-Sobolev spaces

Synthesis and Properties of Oligodeoxynucleotides Carrying 2-Aminopurine

The use of benzoyl, isobutyryl and dimethylaminomethylidene groups for the protection of the exocyclic amino function of 2-aminopurine during oligonucleotide synthesis has been investigated. Best results in the synthesis were obtained with the monomers of 2-aminopurine protected with the isobutyryl groupThis work was supported by the Spanish Ministry of Education (grant CTQ2010-20541) and the Generalitat de Catalunya (2009/SGR/208).Peer reviewe

Synthesis of oligonucleotides carrying fluorescently labelled O6-alkylguanine for measuring hAGT activity

O6-alkylguanine-DNA-alkyltransferase (hAGT) activity provides resistance to cancer chemotherapeutic agents and its inhibition enhances chemotherapy. We herein present the development of a novel fluorescence assay for the detection of hAGT activity. We designed a dsDNA sequence containing a fluorophore-quencher pair, where the fluorophore was attached to an O6-benzylguanine. This precursor was synthesized using the Mitsunobu reaction to introduce the benzyl group. The alkyl-fluorophore group is transferred to the active site during the dealkylation, producing an increase in fluorescence which is correlated to hAGT activity. This assay can be used for the evaluation of potential inhibitors of hAGT in a straightforward manner.The Communities MULTIFUN (contract NMP4-LA-2011-262943), Spanish Healthcare Research Fund (grant PI06/1250) and Spanish Ministry of Economy and Competitiveness (grants CTQ-2010-20541-C03-03 and CTQ2014-52588-R) are acknowledged for financialsupport. M.T. was supported by a pre-doctoral fellowship (FPI) from MINECO. C.F is grateful to TV3 Marato 2012 for a research contract.Peer reviewe