Fractional Integration in Weighted Lebesgue Spaces

2021 ◽  
Vol 56 (2) ◽  
pp. 57-67
Author(s):  
K. Avetisyan
Keyword(s):  
Fractional Integration ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces

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.

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