Related papers: Generalized H\"older's inequality on Morrey spaces
For some class of mappings, which are generalization of space quasiisometries, an upper estimate for a measure of image of a ball is obtained. As consequence, it is obtained one analog of Schwartz lemma for mappings mentioned above. Results…
A priori estimates for the weak solutions the Dirichlet problem for the uniformly higher-order elliptic equations in a smooth bounded domain $\Omega\subset \Rn$ in generalized weighted Sobolev-Morrey spaces are obtained.
We examine the problem of the Fourier transform mapping one weighted Lebesgue space into another, by studying necessary conditions and sufficient conditions which expose an underlying geometry. In the necessary conditions, this geometry is…
Boundedness of an abstract formulation of Hardy operators between Lebesgue spaces over general measure spaces is studied and, when the domain is L^1, shown to be equivalent to the existence of a Hardy inequality on the half line with…
We study the boundedness of intrinsic square functions and their commutators on generalized Orlicz-Morrey spaces $M^{\Phi,\varphi}(\mathbb{R}^n)$. In all the cases the conditions for the boundedness are given either in terms of Zygmund-type…
The Orlicz-Morrey spaces, which were introduced through the research of Nakai in 2006, are a generalization and combination of Orlicz and Morrey spaces. There are two types of Orlicz-Morrey spaces, such as continuous Orlicz-Morrey spaces…
In this note besides two abstract versions of the Vitali Covering Lemma an abstract Hardy-Littlewood Maximal Inequality, generalizing weak type (1,1) maximal function inequality, associated to any outer measure and a family of subsets on a…
The main aim of this paper is to find necessary and sufficient conditions for the convergence of Walsh-Kaczmarz-Fej\'er means in the terms of the modulus of continuity on the Hardy spaces $H_{p},$ when $0<p\leq 1/2.$
In this paper we calculate some geometric constants for Morrey spaces and small Morrey spaces, namely generalized Von Neumann-Jordan constant, modified Von Neumann-Jordan constants, and Zb\'{a}ganu constant. All these constants measure the…
We generalize here the celebrated Partial Regularity Theory of Caffarelli, Kohn and Nirenberg to the MHD equations in the framework of parabolic Morrey spaces. This type of parabolic generalization using Morrey spaces appears to be crucial…
We give an updated extended survey of results related to the celebrated unsolved generalized R. L. Moore problem. In particular, we address the problem of characterizing codimension one manifold factors, i.e. spaces $X$ having the property…
Let $ \mathcal{B}:=\{f(z)=\sum_{n=0}^{\infty}a_nz^n\; \mbox{with}\; |f(z)|<1\;\mbox{for all}\; z\in\mathbb{D}\} $. The improved version of the classical Bohr's inequality \cite{Bohr-1914} states that if $ f\in\mathcal{B} $, then the…
In this paper we discuss the structure of weighted weak Lebesgue spaces and weighted weak Orlicz spaces on $\mathbb{R}^n$. First, we present sufficient and necessary conditions for inclusion relation between weighted weak Lebesgue spaces.…
The goal of this paper is to generalize Demailly's asymptotic holomorphic Morse inequalities to the case of a covering manifold of a compact manifold. We shall obtain estimates which involve Atiyah's ``normalized dimension'' of the square…
The aim of this paper is to provide Markov-type inequalities in the setting of weighted Sobolev spaces when the considered weights are generalized classical weights. Also, as results of independent interest, some basic facts about Sobolev…
Generalised Morrey (function) spaces enjoyed some interest recently and found applications to PDE. Here we turn our attention to their discrete counterparts. We define generalised Morrey sequence spaces…
In this paper we provide mixed weak type inequalities generalizing previous results in an earlier work by Caldarelli and the second author and also in the spirit of earlier results by Lorente, Martell, P\'erez and Riveros. One of the main…
A new inequality between angles in inner product spaces is formulated and proved. It leads directly to a concise statement and proof of the generalized Wielandt inequality, including a simple description of all cases of equality. As a…
In this paper we study some weak majorization properties with applications for the trees. A strongly notion of majorization is introduced and Hardy-Littlewood-Polya's inequality is generalized.
Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.