Hardy Operators on Variable Exponent Spaces

2011 ◽  
pp. 183-209
Author(s):  
Jan Lang ◽  
David Edmunds
Keyword(s):  
Variable Exponent ◽  
Variable Exponent Spaces ◽  
Hardy Operators

scholarly journals Variable Exponent Spaces of Analytic Functions

2020 ◽  
Author(s):  
Gerardo A. Chacón ◽  
Gerardo R. Chacón
Keyword(s):  
Hardy Spaces ◽  
Measurable Function ◽  
Analytic Functions ◽  
Variable Exponent ◽  
Bergman Spaces ◽  
Lebesgue Spaces ◽  
Basic Properties ◽  
Variable Exponent Spaces ◽  
Real Functions ◽  
Spaces Of Analytic Functions

Variable exponent spaces are a generalization of Lebesgue spaces in which the exponent is a measurable function. Most of the research done in this topic has been situated under the context of real functions. In this work, we present two examples of variable exponent spaces of analytic functions: variable exponent Hardy spaces and variable exponent Bergman spaces. We will introduce the spaces together with some basic properties and the main techniques used in the context. We will show that in both cases, the boundedness of the evaluation functionals plays a key role in the theory. We also present a section of possible directions of research in this topic.

scholarly journals A Gamma convergence approach to the critical Sobolev embedding in variable exponent spaces

2016 ◽  
Vol 442 (1) ◽  
pp. 189-205 ◽  
Author(s):  
Julián Fernández Bonder ◽  
Nicolas Saintier ◽  
Analia Silva
Keyword(s):  
Variable Exponent ◽  
Sobolev Embedding ◽  
Gamma Convergence ◽  
Variable Exponent Spaces

scholarly journals A mass transportation approach for Sobolev inequalities in variable exponent spaces

2016 ◽  
Vol 151 (1-2) ◽  
pp. 133-146
Author(s):  
Juan Pablo Borthagaray ◽  
Julián Fernández Bonder ◽  
Analía Silva
Keyword(s):  
Variable Exponent ◽  
Sobolev Inequalities ◽  
Mass Transportation ◽  
Variable Exponent Spaces

scholarly journals Elliptic problems in variable exponent spaces

2006 ◽  
Vol 74 (2) ◽  
pp. 197-206 ◽  
Author(s):  
Mihai Mihailescu
Keyword(s):  
Variational Principle ◽  
Nonlinear Elliptic Equation ◽  
Variable Exponent ◽  
Mountain Pass Theorem ◽  
Growth Conditions ◽  
Cylindrical Symmetry ◽  
Multiplicity Results ◽  
Variable Exponent Spaces ◽  
Nonlinear Elliptic ◽  
Existence And Multiplicity

In this paper we study a nonlinear elliptic equation involving p(x)-growth conditions on a bounded domain having cylindrical symmetry. We establish existence and multiplicity results using as main tools the mountain pass theorem of Ambosetti and Rabinowitz and Ekeland's variational principle.

scholarly journals Riemann-Liouville and Higher Dimensional Hardy Operators for NonNegative Decreasing Function inLp(·)Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Muhammad Sarwar ◽  
Ghulam Murtaza ◽  
Irshaad Ahmed
Keyword(s):  
Integral Operator ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Sufficient Conditions ◽  
Fractional Integral Operator ◽  
Lebesgue Spaces ◽  
Higher Dimensional ◽  
Necessary And Sufficient ◽  
Decreasing Functions ◽  
Hardy Operators

One-weight inequalities with general weights for Riemann-Liouville transform andn-dimensional fractional integral operator in variable exponent Lebesgue spaces defined onRnare investigated. In particular, we derive necessary and sufficient conditions governing one-weight inequalities for these operators on the cone of nonnegative decreasing functions inLp(x)spaces.

scholarly journals Nondivergence parabolic equations in weighted variable exponent spaces

2017 ◽  
Vol 370 (4) ◽  
pp. 2263-2298 ◽  
Author(s):  
Sun-Sig Byun ◽  
Mikyoung Lee ◽  
Jihoon Ok
Keyword(s):  
Parabolic Equations ◽  
Variable Exponent ◽  
Variable Exponent Spaces ◽  
Weighted Variable
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