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 $10$

Bilinear forms on non-homogeneous Sobolev spaces

In this paper we show that if $b\in L^2(\R^n)$, then the bilinear form defined on the product of the non-homogeneous Sobolev spaces $H_s^2(\R^n)\times H_s^2(\R^n)$, $0<s<1$ by $$(f,g)\in H_s^2(\R^n)\times H_s^2(\R^n) \to \int_{\R^n} (Id-\Delta)^{s/2}(fg)({\bf x}) b({\bf x})d{\bf x},$$ is continuous if and only if the positive measure $|b({\bf x})|^2d{\bf x}$ is a trace measure for $H_s^2(\R^n)$

Bilinear forms on potential spaces in the unit circle

In this paper we characterize the boundedness on the product of Sobolev spaces $H^s(\mathbb{T}) \times H^s(\mathbb{T})$ on the unit circle $\mathbb{T}$, of the bilinear form $\Lambda_b$ with symbol $b \in H^s(\mathbb{T})$ given by $$ \Lambda_b(\varphi, \psi):=\int_{\mathbb{T}}\left((-\Delta)^s+I\right)(\varphi \psi)(\eta) b(\eta) d \sigma(\eta)$

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

Platinum (II) and palladium (II) complexes with (N,N') and (C,N,N') ligands derived from pyrazole as anticancer and antimalarial agents: synthesis, characterization and in vitro activities

The study of the reactivity of three 1-(2-dimethylaminoethyl)-1H-pyrazole derivatives of general formula [1-(CH2)2NMe2}-3,5-R2-pzol] {where pzol represents pyrazole and Rdouble bond; length as m-dashH (1a), Me (1b) or Ph (1c)} with [MCl2(DMSO)2] (Mdouble bond; length as m-dashPt or Pd) under different experimental conditions allowed us to isolate and characterize cis-[M{κ2-N,N′-{[1-(CH2)2NMe2}-3,5-R2-pzol])}Cl2] {MMdouble bond; length as m-dashPtPt (2a-2c) or Pd (3a-3c)} and two cyclometallated complexes [M{κ3-C,N,N′-{[1-(CH2)2NMe2}-3-(C5H4)-5-Ph-pzol])}Cl] {Mdouble bond; length as m-dashPt(II) (4c) or Pd(II) (5c)}. Compounds 4c and 5c arise from the orthometallation of the 3-phenyl ring of ligand 1c. Complex 2a has been further characterized by X-ray crystallography. Ligands and complexes were evaluated for their in vitro antimalarial against Plasmodium falciparum and cytotoxic activities against lung (A549) and breast (MDA MB231 and MCF7) cancer cellular lines. Complexes 2a-2c and 5c exhibited only moderate antimalarial activities against two P. falciparum strains (3D7 and W2). Interestingly, cytotoxicity assays revealed that the platinacycle 4c exhibits a higher toxicity than cisplatin in the three human cell lines and that the complex 2a presents a remarkable cytotoxicity and selectivity in lung (IC50 = 3 μM) versus breast cancer cell lines (IC50 > 20 μM). Thus, complexes 2c and 4c appear to be promising leads, creating a novel family of anticancer agents. Electrophoretic DNA migration studies in presence of the synthesized compounds have been performed, in order to get further insights into their mechanism of action

Bilinear forms on weighted Besov spaces

We compute the norm of some bilinear forms on products of weighted Besov spaces in terms of the norm of their symbol in a space of pointwise multipliers related to a space of Carleson measures

A characterization of bilinear forms on the dirichlet space

Arcozzi, Rochberg, Sawyer and Wick obtained a characterization of the holomorphic functions $b$ such that the Hankel type bilinear form $T_{b}(f,g)=\int_{\mathbb{D}}(I+R)(f,g)(z)\overline{(I+R)b(z)}dv (z)$ is bounded on ${\mathcal D}\times {\mathcal D}$, where ${\mathcal D}$ is the Dirichlet space. In this paper we give an alternative proof of this characterization which tries to understand the similarity with the results of Maz$'$ya and Verbitsky relative to the Schrödinger forms on the Sobolev spaces $L_2^1(\mathbb{R}^n)$

Bilinear forms on weighted Besov spaces

We compute the norm of some bilinear forms on products of weighted Besov spaces in terms of the norm of their symbol in a space of pointwise multipliers related to a space of Carleson measures