Moser-Trudinger inequality in grand Lebesgue space

2015 ◽  
Vol 26 (2) ◽  
pp. 177-188 ◽  
Author(s):  
Robert Černý
Keyword(s):  
Lebesgue Space ◽  
Trudinger Inequality ◽  
Grand Lebesgue Space

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.

scholarly journals Duality of fully measurable grand Lebesgue space

2017 ◽  
Vol 171 (1) ◽  
pp. 32-47 ◽  
Author(s):  
Pankaj Jain ◽  
Monika Singh ◽  
Arun Pal Singh
Keyword(s):  
Lebesgue Space ◽  
Grand Lebesgue Space

scholarly journals A Study of Holders Inequality in New Spaces

1970 ◽  
Vol 8 (1-2) ◽  
pp. 259-262
Author(s):  
C. R. Bhatta
Keyword(s):  
Banach Lattice ◽  
Lebesgue Space ◽  
Lattice Space ◽  
Grand Lebesgue Space

The central attraction of this paper is to prove holders inequality in some new spaces such as Grand Lebesgue Space LP). Small Lebesgue space LP)' and Banach Lattice space XP.Key words: Holders InequalityDOI: http://dx.doi.org/10.3126/jie.v8i1-2.5119Journal of the Institute of Engineering Vol. 8, No. 1&2, 2010/2011Page: 259-262Uploaded Date: 20 July, 2011

scholarly journals Relationship Between an Atomic Decomposition of Double and Unary Systems in Grand-Lebesgue Spaces

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Lebesgue Space ◽  
Atomic Decomposition ◽  
Shift Operator ◽  
Continuous Functions ◽  
Lebesgue Spaces ◽  
Grand Lebesgue Spaces ◽  
Separable Subspace ◽  
Grand Lebesgue Space

The grand-Lebesgue space is defined. Based on the shift operator, a separable subspace is determined in which continuous functions are dense. The concepts of frame and atomic decomposition are defined. An atomic decomposition of double and unary systems of functions in grand-Lebesgue spaces is considered. Relationship between atomic decomposition of these systems in grand-Lebesgue spaces is established

Boundedness of weighted singular integral operators in grand Lebesgue spaces

2011 ◽  
Vol 18 (2) ◽  
pp. 259-269
Author(s):  
Vakhtang Kokilashvili ◽  
Stefan Samko
Keyword(s):  
Singular Integral ◽  
Lebesgue Space ◽  
Sufficient Conditions ◽  
Singular Integral Equations ◽  
Lebesgue Spaces ◽  
Grand Lebesgue Spaces ◽  
Carleson Curve ◽  
Power Weights ◽  
Necessary And Sufficient ◽  
Grand Lebesgue Space

Abstract We obtain the necessary and sufficient conditions for the boundedness of the weighted singular integral operator with power weights in grand Lebesgue spaces. Because of applications to singular integral equations, the underlying set on which the functions are defined is a Carleson curve in the complex plane. Note that weighted boundedness of an operator in grand Lebesgue space is not the same as the boundedness in weighted grand Lebesgue space.

scholarly journals The Distance toL∞in the Grand Orlicz Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Fernando Farroni ◽  
Raffaella Giova
Keyword(s):  
Orlicz Space ◽  
Lebesgue Space ◽  
Orlicz Spaces ◽  
New Formula ◽  
Grand Lebesgue Space

We establish a formula for the distance toL∞from the grand Orlicz spaceLΦ)Ωintroduced in Capone et al. (2008). A new formula for the distance toL∞from the grand Lebesgue spaceLn)Ωintroduced in Iwaniec and Sbordone (1992) is also provided.

A Note on the Boundedness of the Hilbert Transform in Weighted Grand Lebesgue Spaces

2009 ◽  
Vol 16 (3) ◽  
pp. 547-551 ◽  
Author(s):  
Vakhtang Kokilashvili ◽  
Alexander Meskhi
Keyword(s):  
Hilbert Transform ◽  
Lebesgue Space ◽  
Finite Interval ◽  
Lebesgue Spaces ◽  
Grand Lebesgue Spaces ◽  
Muckenhoupt Condition ◽  
The Hilbert Transform ◽  
Grand Lebesgue Space

Abstract It is proved that the Hilbert transform defined on a finite interval is bounded in the grand Lebesgue space if and only if 𝑤 satisfies the Muckenhoupt condition 𝐴𝑝.

scholarly journals A Decomposition of the Dual Space of Some Banach Function Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Claudia Capone ◽  
Maria Rosaria Formica
Keyword(s):  
Lebesgue Space ◽  
Dual Space ◽  
Function Spaces ◽  
Zygmund Space ◽  
Marcinkiewicz Space ◽  
Banach Function Spaces ◽  
Integrable Functions ◽  
Grand Lebesgue Space

We give a decomposition for the dual space of some Banach Function Spaces as the Zygmund space of the exponential integrable functions, the Marcinkiewicz space , and the Grand Lebesgue Space .

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