scholarly journals Solvability in weighted Lebesgue spaces of the divergence equation with measure data

2021 ◽  
Author(s):  
Laurent Moonens ◽  
Emmanuel Russ
Keyword(s):  
Measure Data ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces ◽  
Divergence Equation

scholarly journals Sharp bounds for general commutators on weighted Lebesgue spaces

2012 ◽  
Vol 364 (3) ◽  
pp. 1163-1177 ◽  
Author(s):  
Daewon Chung ◽  
M. Cristina Pereyra ◽  
Carlos Perez
Keyword(s):  
Lebesgue Spaces ◽  
Sharp Bounds ◽  
Weighted Lebesgue Spaces

scholarly journals Convolution Algebraic Structures Defined by Hardy-Type Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Pedro J. Miana ◽  
Juan J. Royo ◽  
Luis Sánchez-Lajusticia
Keyword(s):  
Sobolev Spaces ◽  
Banach Algebras ◽  
Weighted Sobolev Spaces ◽  
Integral Kernel ◽  
Lebesgue Spaces ◽  
Hardy Type ◽  
Weighted Lebesgue Spaces ◽  
Banach Modules ◽  
Hardy Type Operator ◽  
Fractional Derivation

The main aim of this paper is to show that certain Banach spaces, defined via integral kernel operators, are Banach modules (with respect to some known Banach algebras and convolution products onℝ+). To do this, we consider some suitable kernels such that the Hardy-type operator is bounded in weighted Lebesgue spacesLωpℝ+forp≥1. We also show new inequalities in these weighted Lebesgue spaces. These results are applied to several concrete function spaces, for example, weighted Sobolev spaces and fractional Sobolev spaces defined by Weyl fractional derivation.

The Chen-Marchaud fractional integro-differentiation in the variable exponent Lebesgue spaces

2011 ◽  
Vol 14 (3) ◽  
Author(s):  
Humberto Rafeiro ◽  
Makhmadiyor Yakhshiboev
Keyword(s):  
Integral Operator ◽  
Fractional Derivative ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Inverse Operator ◽  
Fractional Integral Operator ◽  
Left Inverse ◽  
Fractional Differentiation ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces

AbstractAfter recalling some definitions regarding the Chen fractional integro-differentiation and discussing the pro et contra of various ways of truncation related to Chen fractional differentiation, we show that, within the framework of weighted Lebesgue spaces with variable exponent, the Chen-Marchaud fractional derivative is the left inverse operator for the Chen fractional integral operator.

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