scholarly journals Hardy type operators on grand Lebesgue spaces for non-increasing functions

2016 ◽  
Vol 170 (1) ◽  
pp. 34-46 ◽  
Author(s):  
Pankaj Jain ◽  
Monika Singh ◽  
Arun Pal Singh
Keyword(s):  
Lebesgue Spaces ◽  
Hardy Type ◽  
Grand Lebesgue Spaces ◽  
Increasing Functions ◽  
Hardy Type Operators

Hardy-type integral inequalities for quasi-monotone functions

2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Pankaj Jain ◽  
Monika Singh ◽  
Arun Pal Singh
Keyword(s):  
Integral Inequalities ◽  
Monotone Functions ◽  
Lebesgue Spaces ◽  
Hardy Type ◽  
Grand Lebesgue Spaces ◽  
Type Integral

AbstractWe consider quasi-monotone functions and discuss various Hardy-type integral inequalities on weighted Lebesgue and grand Lebesgue spaces.

Hardy type inequalities in generalized grand Lebesgue spaces

2021 ◽  
Vol 6 (2) ◽  
Author(s):  
Joel E. Restrepo ◽  
Durvudkhan Suragan
Keyword(s):  
Lebesgue Spaces ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Grand Lebesgue Spaces

On Hardy type inequalities in grand Lebesgue spaces Lp) for 0 < p ≤ 1

2021 ◽  
pp. 1-14
Author(s):  
Rovshan A. Bandaliyev ◽  
Kamala H. Safarova
Keyword(s):  
Lebesgue Spaces ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Grand Lebesgue Spaces

Compactness of Hardy-Type Operators over Star-Shaped Regions in

2004 ◽  
Vol 47 (4) ◽  
pp. 540-552 ◽  
Author(s):  
Pankaj Jain ◽  
Pawan K. Jain ◽  
Babita Gupta
Keyword(s):  
Compactness Property ◽  
Lebesgue Spaces ◽  
Hardy Type ◽  
Weighted Lebesgue Spaces ◽  
Hardy Type Operators

AbstractWe study a compactness property of the operators between weighted Lebesgue spaces that average a function over certain domains involving a star-shaped region. The cases covered are (i) when the average is taken over a difference of two dilations of a star-shaped region in , and (ii) when the average is taken over all dilations of star-shaped regions in . These cases include, respectively, the average over annuli and the average over balls centered at origin.

scholarly journals Гранд-пространства типа Морри

2020 ◽  
pp. 104-118
Author(s):  
S.G. Samko ◽  
S.M. Umarkhadzhiev
Keyword(s):  
Integral Operators ◽  
Finite Measure ◽  
Morrey Spaces ◽  
Function Spaces ◽  
Lebesgue Spaces ◽  
Hardy Type ◽  
Grand Lebesgue Spaces ◽  
Type Spaces

The so called grand spaces nowadays are one of the main objects in the theory of function spaces. Grand Lebesgue spaces were introduced by T. Iwaniec and C. Sbordone in the case of sets $\Omega$ with finite measure $|\Omega|<\infty$, and by the authors in the case $|\Omega|=\infty$. The latter is based on introduction of the notion of grandizer. The idea of "grandization" was also applied in the context of Morrey spaces. In this paper we develop the idea of grandization to more general Morrey spaces $L^{p,q,w}(\mathbb{R}^n)$, known as Morrey type spaces. We introduce grand Morrey type spaces, which include mixed and partial grand versions of such spaces. The mixed grand space is defined by the norm $$ \sup_{\varepsilon,\delta} \varphi(\varepsilon,\delta)\sup_{x\in E} \left(\int\limits_{0}^{\infty}{w(r)^{q-\delta}}b(r)^{\frac{\delta}{q}} \left(\,\int\limits_{|x-y|<r}\big|f(y)\big|^{p-\varepsilon} a(y)^{\frac{\varepsilon}{p}}\,dy\right)^{\frac{q-\delta}{p-\varepsilon}} \frac{dr}{r}\right)^{\frac{1}{q-\varepsilon}} $$ with the use of two grandizers $a$ and $b$. In the case of grand spaces, partial with respect to the exponent $q$, we study the boundedness of some integral operators. The class of these operators contains, in particular, multidimensional versions of Hardy type and Hilbert operators.

Hardy-type Operators in Variable Exponent Lebesgue Spaces

2016 ◽  
pp. 1-26 ◽  
Author(s):  
Vakhtang Kokilashvili ◽  
Alexander Meskhi ◽  
Humberto Rafeiro ◽  
Stefan Samko
Keyword(s):  
Variable Exponent ◽  
Lebesgue Spaces ◽  
Hardy Type ◽  
Variable Exponent Lebesgue Spaces ◽  
Hardy Type Operators

Trace inequalities for fractional integrals in mixed norm grand lebesgue spaces

2020 ◽  
Vol 23 (5) ◽  
pp. 1452-1471
Author(s):  
Vakhtang Kokilashvili ◽  
Alexander Meskhi
Keyword(s):  
Riesz Potential ◽  
Fractional Integrals ◽  
Mixed Norm ◽  
Lebesgue Spaces ◽  
Fractional Integral Operators ◽  
Grand Lebesgue Spaces ◽  
Measure Spaces ◽  
Necessary And Sufficient ◽  
Bounded Sets ◽  
Trace Inequalities

Abstract D. Adams type trace inequalities for multiple fractional integral operators in grand Lebesgue spaces with mixed norms are established. Operators under consideration contain multiple fractional integrals defined on the product of quasi-metric measure spaces, and one-sided multiple potentials. In the case when we deal with operators defined on bounded sets, the established conditions are simultaneously necessary and sufficient for appropriate trace inequalities. The derived results are new even for multiple Riesz potential operators defined on the product of Euclidean spaces.

scholarly journals The Approximation Numbers of Hardy-Type Operators on Trees

2001 ◽  
Vol 83 (2) ◽  
pp. 390-418 ◽  
Author(s):  
W. D. Evans ◽  
D. J. Harris ◽  
J. Lang
Keyword(s):  
Approximation Numbers ◽  
Hardy Type ◽  
Hardy Type Operators

Approximation by trigonometric polynomials in the framework of variable exponent grand Lebesgue spaces

2016 ◽  
Vol 23 (1) ◽  
Author(s):  
Nina Danelia ◽  
Vakhtang Kokilashvili
Keyword(s):  
Lebesgue Space ◽  
Variable Exponent ◽  
Trigonometric Polynomials ◽  
Lebesgue Spaces ◽  
Variable Exponent Lebesgue Space ◽  
Grand Lebesgue Spaces ◽  
Direct And Inverse Theorems ◽  
Inverse Theorems ◽  
Grand Lebesgue Space

AbstractIn this paper we establish direct and inverse theorems on approximation by trigonometric polynomials for the functions of the closure of the variable exponent Lebesgue space in the variable exponent grand Lebesgue space.

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