Generalized Concentration-Compactness Principles for Variable Exponent Lebesgue Spaces with Asymptotic Analysis of Low Energy Extremals

Zia Bashir; Juan Luis García Guirao; Adil Siddique; Tareq Saeed

doi:10.3390/math8101849

Generalized Concentration-Compactness Principles for Variable Exponent Lebesgue Spaces with Asymptotic Analysis of Low Energy Extremals

Mathematics ◽

10.3390/math8101849 ◽

2020 ◽

Vol 8 (10) ◽

pp. 1849

Author(s):

Zia Bashir ◽

Juan Luis García Guirao ◽

Adil Siddique ◽

Tareq Saeed

Keyword(s):

Asymptotic Analysis ◽

Asymptotic Behaviour ◽

Variable Exponent ◽

Low Energy ◽

Concentration Compactness ◽

Lebesgue Spaces ◽

Application Study ◽

Variable Exponent Lebesgue Spaces

In this paper, we prove two generalized concentration-compactness principles for variable exponent Lebesgue spaces and as an application study the asymptotic behaviour of low energy extremals.

Maximal and Calderón–Zygmund operators in grand variable exponent Lebesgue spaces

Georgian Mathematical Journal ◽

10.1515/gmj-2014-0047 ◽

2014 ◽

Vol 21 (4) ◽

Cited By ~ 6

Author(s):

Vakhtang Kokilashvili ◽

Alexander Meskhi

Keyword(s):

Variable Exponent ◽

Function Spaces ◽

Lebesgue Spaces ◽

Variable Exponent Lebesgue Spaces

AbstractNew function spaces

Notes on commutator on the variable exponent Lebesgue spaces

10.21136/cmj.2019.0590-17 ◽

2019 ◽

Vol 69 (4) ◽

pp. 1029-1037

Author(s):

Dinghuai Wang

Keyword(s):

Variable Exponent ◽

Lebesgue Spaces ◽

Variable Exponent Lebesgue Spaces

Generalized potentials in variable exponent Lebesgue spaces on homogeneous spaces

Mathematische Nachrichten ◽

10.1002/mana.200710204 ◽

2011 ◽

Vol 284 (1) ◽

pp. 53-66 ◽

Cited By ~ 4

Author(s):

Mubariz G. Hajibayov ◽

Stefan Samko

Keyword(s):

Variable Exponent ◽

Homogeneous Spaces ◽

Lebesgue Spaces ◽

Variable Exponent Lebesgue Spaces

The Boundedness of Multilinear Fractional Integral Operators with Variable Kernel on Variable Exponent Lebesgue Spaces

Pure Mathematics ◽

10.12677/pm.2016.61011 ◽

2016 ◽

Vol 06 (01) ◽

pp. 72-80

Author(s):

秋阅万

Keyword(s):

Variable Exponent ◽

Fractional Integral ◽

Integral Operators ◽

Lebesgue Spaces ◽

Variable Kernel ◽

Fractional Integral Operators ◽

Multilinear Fractional Integral ◽

Variable Exponent Lebesgue Spaces

Estimates of Fractional Integral Operators on Variable Exponent Lebesgue Spaces

Journal of Function Spaces ◽

10.1155/2016/2438157 ◽

2016 ◽

Vol 2016 ◽

pp. 1-7

Author(s):

Canqin Tang ◽

Qing Wu ◽

Jingshi Xu

Keyword(s):

Integral Operator ◽

Maximal Operator ◽

Variable Exponent ◽

Fractional Integral ◽

Weak Type ◽

Type Inequality ◽

Integral Operators ◽

Lebesgue Spaces ◽

Fractional Integral Operators ◽

Variable Exponent Lebesgue Spaces

By some estimates for the variable fractional maximal operator, the authors prove that the fractional integral operator is bounded and satisfies the weak-type inequality on variable exponent Lebesgue spaces.

Variable Exponent Lebesgue Spaces and Hardy-Littlewood Maximal Function on p-Adic Numbers

P-Adic Numbers Ultrametric Analysis and Applications ◽

10.1134/s2070046620020028 ◽

2020 ◽

Vol 12 (2) ◽

pp. 90-111

Author(s):

Leonardo Fabio Chacón-Cortés ◽

Humberto Rafeiro

Keyword(s):

Maximal Function ◽

Variable Exponent ◽

Lebesgue Spaces ◽

Littlewood Maximal Function ◽

Variable Exponent Lebesgue Spaces

Odd asymmetric factorization of Wiener-Hopf plus Hankel operators on variable exponent Lebesgue spaces

10.1063/1.4972630 ◽

2017 ◽

Author(s):

L. P. Castro ◽

A. S. Silva

Keyword(s):

Variable Exponent ◽

Hankel Operators ◽

Lebesgue Spaces ◽

Variable Exponent Lebesgue Spaces

Commutators of the fractional maximal function on variable exponent Lebesgue spaces

Czechoslovak Mathematical Journal ◽

10.1007/s10587-014-0093-x ◽

2014 ◽

Vol 64 (1) ◽

pp. 183-197 ◽

Cited By ~ 17

Author(s):

Pu Zhang ◽

Jianglong Wu

Keyword(s):

Maximal Function ◽

Variable Exponent ◽

Lebesgue Spaces ◽

Fractional Maximal Function ◽

Variable Exponent Lebesgue Spaces

Multilinear singular integrals and commutators in variable exponent Lebesgue spaces

Applied Mathematics-A Journal of Chinese Universities ◽

10.1007/s11766-010-2167-3 ◽

2010 ◽

Vol 25 (1) ◽

pp. 69-77 ◽

Cited By ~ 13

Author(s):

Ai-wu Huang ◽

Jing-shi Xu

Keyword(s):

Variable Exponent ◽

Singular Integrals ◽

Lebesgue Spaces ◽

Variable Exponent Lebesgue Spaces ◽

Multilinear Singular Integrals

The Riemann boundary value problem in the class of Cauchy type integrals with densities of grand variable exponent Lebesgue spaces

Georgian Mathematical Journal ◽

10.1515/gmj-2016-0041 ◽

2016 ◽

Vol 23 (4) ◽

pp. 551-558 ◽

Cited By ~ 1

Author(s):

Vakhtang Kokilashvili ◽

Alexander Meskhi ◽

Vakhtang Paatashvili

Keyword(s):

Boundary Value Problem ◽

Variable Exponent ◽

Boundary Value ◽

Function Spaces ◽

Cauchy Type ◽

Riemann Boundary Value Problem ◽

Lebesgue Spaces ◽

Standard Type ◽

Riemann Boundary ◽

Variable Exponent Lebesgue Spaces

AbstractThe present paper deals with the Riemann boundary value problem for analytic functions in the framework of the new function spaces introduced by the first two authors, the so-called grand variable exponent Lebesgue spaces which unify two non-standard type function spaces: variable exponent Lebesgue spaces and grand Lebesgue spaces.