Related papers: Norm inequalities in generalized Morrey spaces

In this paper, we will study the boundedness properties of multilinear Calderon--Zygmund operators and multilinear fractional integrals on products of weighted Morrey spaces with multiple weights.

In this paper it is shown that the Hardy-Littlewood maximal operator $M$ is not bounded on Zygmund-Morrey space $\mathcal{M}_{L(\log L),\lambda}$, but $M$ is still bounded on $\mathcal{M}_{L(\log L),\lambda}$ for radially decreasing…

The boundedness of the Marcinkiewicz integrals associated with Schr\"{o}dinger operator from the localized Morrey-Campanato space to the localized Morrey-Campanato-BLO space is established. Similar results for the Marcinkiewicz integrals…

Suppose $L=-\Delta+V$ is a Schr\"odinger operator on $\mathbb{R}^n$ with a potential $V$ belonging to certain reverse H\"older class $RH_\sigma$ with $\sigma\geq n/2$. The main aim of this paper is to provide necessary and sufficient…

We consider generalized Orlicz-Morrey spaces $M_{\Phi,\varphi}(\mathbb{R}^{n})$ including their weak versions $WM_{\Phi,\varphi}(\mathbb{R}^{n})$. We find the sufficient conditions on the pairs $(\varphi_{1},\varphi_{2})$ and $(\Phi, \Psi)$…

We prove that a large class of operators, which arise as the projections of martingale transforms of stochastic integrals with respect to Brownian motion, as well as other closely related operators, are in fact Calder\'on--Zygmund…

The bidual of the closure of smooth functions with respect to the Morrey norm coincides with the Morrey space. This assertion is generalized to some Muckenhoupt weighted Morrey spaces. We combine this fact with basic extrapolation…

The recent proof of the sharp weighted bound for Calder\'on-Zygmund operators has led to much investigation in sharp mixed bounds for operators and commutators, that is, a sharp weighted bound that is a product of at least two different…

Let $T$ be a $m$-linear Calder\'{o}n-Zygmund operator of type $\omega$ with $\omega$ being nondecreasing and $\omega \in$ Dini(1) and $[\vec{b},\,T]$ be the commutator generated by $T$ with symbols $\vec{b}=(b_1,\,\ldots,\,b_m)$ belonging…

In this paper, we introduce a discrete version of weighted Morrey spaces, and discuss the inclusion relations of these spaces. In addition, we obtain the boundedness of discrete weighted Hardy-Littlewood maximal operators on discrete…

In a previous work, "compact versions" of Rubio de Francia's weighted extrapolation theorem were proved, which allow one to extrapolate the compactness of an linear operator from just one space to the full range of weighted Lebesgue spaces,…

In this paper, we obtain the boundedness of $m$th order commutators generated by the $n$-dimensional fractional Hardy operator with rough kernel and its adjoint operator with BMO functions on two weighted grand Herz-Morrey spaces with…

We consider a generalization of the Riesz operator in $R^d$ and obtain estimates for its norm and for related capacities via the modified Wolff potential. These estimates are based on the certain version of $T1$ theorem for…

We consider the global Morrey-type spaces with variable exponents and general function defining these spaces. In the case of unbounded sets, we prove boundedness of the Hardy-Littlewood maximal operator, potential type operator in these…

In this paper, the author establishes the boundedness of parametric Littlewood-Paley operators from Musielak-Orlicz Hardy space to Musielak-Orlicz space, or to weak Musielak-Orlicz space at the critical index. Part of these results are new…

In this paper we prove some sharp weighted norm inequalities for the multi(sub)linear maximal function $\Mm$ introduced in \cite{LOPTT} and for multilinear Calder\'on-Zygmund operators. In particular we obtain a sharp mixed…

We study the weighted boundedness of the Cauchy singular integral operator $S_\Gm$ in Morrey spaces $L^{p,\lambda}(\Gm)$ on curves satisfying the arc-chord condition, for a class of "radial type" almost monotonic weights. The non-weighted…

Kernel theorems, in general, provide a convenient representation of bounded linear operators. For the operator acting on a concrete function space, this means that its action on any element of the space can be expressed as a generalised…

We provide a natural BMO-criterion for the $L_2$-boundedness of Calder\'on-Zygmund operators with operator-valued kernels satisfying a symmetric property. Our arguments involve both classical and quantum probability theory. In the appendix,…

In this paper, the authors prove the boundedness of commutators generated by the weighted Hardy operator on weighted $\lambda$-central Morrey space with the weight $\omega$ satisfying the doubling condition. Moreover, the authors give the…