Hölder's inequalities and multilinear singular integrals on generalized Orlicz spaces
type: Item
instance of: scholarly article
title: Hölder's inequalities and multilinear singular integrals on generalized Orlicz spaces
author: Songbai Wang
published in: Journal of Mathematical Inequalities
publication date: 2024-10-15T00:00:00Z
review text: In the paper, a generalized version of Hölder's inequality in the framework of generalized Orlicz spaces is stated. The inequality in question is \N\[\N\big\|\prod_{j=1}^m f_j \big\|_{L^{\varphi(\cdot)}(\mathbb{R}^n)}\le C \prod_{j=1}^m \|f_j \|_{L^{\varphi_j(\cdot)}(\mathbb{R}^n)}. \N\]\NHere \(\varphi_j\in \Phi_w(\mathbb{R}^n)\) for \(j=1,\ldots, m\), \(\Phi_w(\mathbb{R}^n)\) stand for the so-called class of generalized (weak) \(\Phi\)-functions, and \(\varphi=(\prod_{j=1}^m \varphi_j^{-1})^{-1}\) (appropriately defined) is the so-called left-inverse. Moreover, \(\|\cdot\|_{L^{\varphi(\cdot)}(\mathbb{R}^n)}\) and \(\|\cdot\|_{L^{\varphi_j(\cdot)}(\mathbb{R}^n)}\) denote the norms in the generalized Orlicz spaces accordingly defined for functions \(\varphi\) and \(\varphi_j\), respectively.
reviewed by: Krzysztof Stempak
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 7926204
zbMATH Keywords: Hölder inequality
zbMATH Keywords: genearlized Orlicz space
zbMATH Keywords: multilinear singular integral
MaRDI profile type: Publication
cites work: On some new non-linear diffusion models for the image filtering
cites work: Harnack inequalities for double phase functionals
cites work: Non-autonomous functionals, borderline cases and related function classes
cites work: The spaces \(L^ p\), with mixed norm
cites work: Q4039801
cites work: Variable Exponent, Linear Growth Functionals in Image Restoration
cites work: On Commutators of Singular Integrals and Bilinear Singular Integrals
cites work: Q3941791
cites work: Polynomial growth estimates for multilinear singular integral operators
cites work: Bounded minimisers of double phase variational integrals
cites work: Extrapolation and interpolation in generalized Orlicz spaces
cites work: Sharp weighted bounds for multilinear maximal functions and Calderón-Zygmund operators
cites work: Lebesgue and Sobolev spaces with variable exponents
cites work: Regularity results for a new class of functionals with non-standard growth conditions
cites work: On multilinear fractional integrals
cites work: Multilinear Calderón-Zygmund theory
cites work: Maximal operator and weighted norm inequalities for multilinear singular integrals
cites work: Orlicz spaces and generalized Orlicz spaces
cites work: The Riesz potential in generalized Orlicz spaces
cites work: Generalized Orlicz spaces and related PDE
cites work: Critical variable exponent functionals in image restoration
cites work: The maximal operator on generalized Orlicz spaces
cites work: Calderón-Zygmund estimates in generalized Orlicz spaces
cites work: Multilinear singular integrals and commutators in variable exponent Lebesgue spaces
cites work: Sharp bounds for multilinear fractional integral operators on Morrey type spaces
cites work: Multilinear estimates and fractional integration
cites work: Q4021390
cites work: New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory
cites work: Sparse domination theorem for multilinear singular integral operators with \(L^r\)-Hörmander condition
cites work: The sharp weighted bound for multilinear maximal functions and Calderón-Zygmund operators
cites work: Weak and strong type weighted estimates for multilinear Calderón-Zygmund operators
cites work: Why Hölder's inequality should be called Rogers' inequality
cites work: Weighted inequalities for multilinear fractional integral operators
cites work: New weighted estimates for bilinear fractional integral operators
cites work: Orlicz spaces and modular spaces
cites work: Q5801558
cites work: Über konjugierte Exponentenfolgen
cites work: Weighted inequalities and pointwise estimates for the multilinear fractional integral and maximal operators
cites work: Q4000065
cites work: Nonlinear parabolic problems in Musielak-Orlicz spaces
cites work: Multilinear singular and fractional integral operators on weighted Morrey spaces
DOI: 10.7153/JMI-2024-18-44
description: scientific article; zbMATH DE number 7926204