Some translation-invariant Banach function spaces which contain $c_0$ [PDF]
Studia Mathematica 163, 2 (2004) 137 - 155, 2009 We produce several situations where some natural subspaces of classical Banach spaces of functions over a compact abelian group contain the space $c_0$.
arxiv
Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces [PDF]
arXiv, 2012 We prove optimal integrability results for solutions of the $p(\cdot)$-Laplace equation in the scale of (weak) Lebesgue spaces. To obtain this, we show that variable exponent Riesz and Wolff potentials maps $L^1$ to variable exponent weak Lebesgue spaces.
arxiv
The class Bp for weighted generalized Fourier transform inequalities [PDF]
arXiv, 2013 In the present paper, we prove for the Dunkl transform which generalizes the Fourier transform, weighted inequalities when the weights belong to the well known class Bp. As application, we obtain for power weights Pitt's inequality.
arxiv
Pointwise multipliers on martingale Campanato spaces [PDF]
arXiv, 2013 We introduce generalized Campanato spaces $\mathcal{L}_{p,\phi}$ on a probability space $(\Omega,\mathcal{F},P)$, where $p\in[1,\infty)$ and $\phi:(0,1]\to(0,\infty)$. If $p=1$ and $\phi\equiv1$, then $\mathcal{L}_{p,\phi}=\mathrm{BMO}$. We give a characterization of the set of all pointwise multipliers on $\mathcal{L}_{p,\phi}$.
arxiv
Compactness in the Lebesgue-Bochner spaces L^p(μ;X) [PDF]
arXiv, 2013 Let (\Omega,\mu) be a finite measure space, X a Banach space, and let 1\le p<\infty. The aim of this paper is to give an elementary proof of the Diaz--Mayoral theorem that a subset V of L^p(\mu;X) is relatively compact if and only if it is uniformly p-integrable, uniformly tight, and scalarly relatively compact.
arxiv
Maximal potentials, maximal singular integrals, and the spherical maximal function [PDF]
arXiv, 2013 We introduce a notion of maximal potentials and we prove that they form bounded operators from $L^p$ to the homogeneous Sobolev space $\dot{W}^{1,p}$ for all $n/(n-1)
arxiv
Associated Spaces of Generalized Classical Lorentz Spaces $GΛ_{p,ψ;\varphi}$ [PDF]
arXiv, 2013 In this paper we have calculated the associate norms of the $G\Lambda_{p,\psi;\varphi}$ generalized classical Lorentz spaces.
arxiv
Fractional integrals and Fourier transforms [PDF]
arXiv, 2017 This paper gives a short survey of some basic results related to estimates of fractional integrals and Fourier transforms. It is closely adjoint to our previous survey papers \cite{K1998} and \cite{K2007}. The main methods used in the paper are based on nonincreasing rearrangements. We give alternative proofs of some results. We observe also that the
arxiv
Related searches:
Gradient estimates in anisotropic Lorentz spaces to general elliptic equations of p-growth
Rocky Mountain Journal of Mathematics, 2022We prove a global mixed-norm gradient estimate in the framework of anisotropic Lorentz spaces to general elliptic equations of p-growth under weak regularity data.
H. Tian, Shenzhou Zheng
semanticscholar +1 more source
Erdélyi–Kober fractional integral operators on ball Banach function spaces
, 2021We establish the boundedness of the Erdélyi-Kober fractional integral operators on ball Banach function spaces. In particular, it gives the boundedness of the Erdélyi-Kober fractional integral operators on amalgam spaces and Morrey spaces.
K. Ho
semanticscholar +1 more source