Related papers: Boundedness of area operators on Bergman spaces

We prove boundedness results for integral operators of fractional type and their higher order commutators between weighted spaces, including $L^p$-$L^q$, $L^p$-$BMO$ and $L^p$-Lipschitz estimates. The kernels of such operators satisfy…

In the context of variable exponent Lebesgue spaces equipped with a lower Ahlfors measure we obtain weighted norm inequalities over bounded domains for the centered fractional maximal function and the fractional integral operator.

We consider a class of two-parameter weighted integral operators induced by harmonic Bergman-Besov kernels on the unit ball of $\mathbb{R}^{n}$ and characterize precisely those that are bounded from Lebesgue spaces $L^{p}_{\alpha}$ into…

For $1<p<\infty$, we prove the $L^p$-boundedness of the Riesz transform operators on metric measure spaces with Riemannian Ricci curvature bounded from below, without any restriction on their dimension. This large class of spaces include…

In this paper we prove necessary conditions for the boundedness of fractional operators on the variable Lebesgue spaces. More precisely, we find necessary conditions on an exponent function $\pp$ for a fractional maximal operator $M_\alpha$…

We prove that operators satisfying the hypotheses of the extrapolation theorem for Muckenhoupt weights are bounded on weighted Morrey spaces. As a consequence, we obtain at once a number of results that have been proved individually for…

Let $S_n f$ be the $n$th partial sum of the Fourier series of a function $f$ in $L^1(\D)$, where $\D$ is the ring of integers of a local field $K$. For $1<p<\infty$, we characterize all weight functions $w$ so that the partial sum operators…

We study two classes of bounded operators on mixed norm Lebesgue spaces, namely composition operators and product operators. A complete description of bounded composition operators on mixed norm Lebesgue spaces are given. For a certain…

Let $A_{\alpha}^{p}(\mathbb{B}^n;\mathbb{C}^d)$ be the weighted Bergman space on the unit ball $\mathbb{B}^n$ of $\mathbb{C}^n$ of functions taking values in $\mathbb{C}^d$. For $1<p<\infty$ let $\mathcal{T}_{p,\alpha}$ be the algebra…

Supplying the missing necessary conditions, we complete the characterisation of the $L^p\to L^q$ boundedness of commutators $[b,T]$ of pointwise multiplication and Calder\'on-Zygmund operators, for arbitrary pairs of $1<p,q<\infty$ and…

We prove that, for arbitrary centres and strengths, the wave operators for three dimensional Schr\"odinger operators with multi-centre local point interactions are bounded in $L^p(\mathbb{R}^3)$ for $1<p<3$ and unbounded otherwise.

If $\mu$ is a finite measure on the unit disc and $k\ge 0$ is an integer, we study a generalization derived from Englis's work, $T_\mu^{(k)}$, of the traditional Toeplitz operators on the Bergman space $A^2$, which are the case $k=0$. Among…

Let $A$ be an unbounded operator on a Banach space $X$. It is sometimes useful to improve the operator $A$ by extending it to an operator $B$ on a larger Banach space $Y$ with smaller spectrum. It would be preferable to do this with some…

We characterize the semigroups of composition operators that are strongly continuous on the mixed norm spaces $H(p,q,\alpha)$. First, we study the separable spaces $H(p,q,\alpha)$ with $q<\infty,$ that behave as the Hardy and Bergman…

We prove the Lorentz-Shimogaki and Boyd theorems for the spaces $\Lambda^p_u(w)$. As a consequence, we give the complete characterization of the strong boundedness of $H$ on these spaces in terms of some geometric conditions on the weights…

In this work we establish sharp boundedness results for pseudo-differential operators corresponding to $a\in\mathcal{S}_{0,0}^{m}$ on Triebel-Lizorkin spaces $F_p^{s,q}$ and Besov spaces $B_p^{s,q}$.

We investigate the global boundedness of Fourier integral operators with amplitudes in the general H\"ormander classes $S^{m}_{\rho, \delta}(\mathbb{R}^n)$, $\rho, \delta\in [0,1]$ and non-degenerate phase functions of arbitrary rank…

In this paper, we consider the weighted Hardy space $\mathcal{H}^p(\omega)$ induced by an $A_1$ weight $\omega.$ We characterize the positive Borel measure $\mu$ such that the identical operator maps $\mathcal{H}^p(\omega)$ into $L^q(d\mu)$…

This paper investigates the concept of the $q$-Berezin range and $q$-Berezin number of bounded linear operators acting on Hardy space. We obtain the $q$-Berezin range of some classes of operators on Hardy space. In addition, the convexity…

It is known that Fourier integral operators arising when solving Schr\"odinger-type operators are bounded on the modulation spaces $\cM^{p,q}$, for $1\leq p=q\leq\infty$, provided their symbols belong to the Sj\"ostrand class…