Maximal function on generalized martingale Lebesgue spaces with variable exponent

2013 ◽  
Vol 83 (10) ◽  
pp. 2168-2171 ◽  
Author(s):  
Eiichi Nakai ◽  
Gaku Sadasue
Keyword(s):  
Maximal Function ◽  
Variable Exponent ◽  
Lebesgue Spaces ◽  
Generalized Martingale

scholarly journals Weighted and endpoint estimates for commutators of bilinear pseudo-differential operators

2022 ◽  
Vol 7 (4) ◽  
pp. 5971-5990
Author(s):  
Yanqi Yang ◽  
◽  
Shuangping Tao ◽  
Guanghui Lu
Keyword(s):  
Maximal Function ◽  
Lipschitz Function ◽  
Variable Exponent ◽  
Differential Operators ◽  
Sharp Maximal Function ◽  
Pointwise Estimates ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces ◽  
Variable Exponent Lebesgue Spaces ◽  
Pseudo Differential Operators

<abstract><p>In this paper, by applying the accurate estimates of the Hörmander class, the authors consider the commutators of bilinear pseudo-differential operators and the operation of multiplication by a Lipschitz function. By establishing the pointwise estimates of the corresponding sharp maximal function, the boundedness of the commutators is obtained respectively on the products of weighted Lebesgue spaces and variable exponent Lebesgue spaces with $ \sigma \in\mathcal{B}BS_{1, 1}^{1} $. Moreover, the endpoint estimate of the commutators is also established on $ L^{\infty}\times L^{\infty} $.</p></abstract>

scholarly journals A note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spaces

2021 ◽  
Vol 19 (1) ◽  
pp. 306-315
Author(s):  
Esra Kaya
Keyword(s):  
Differential Operator ◽  
Maximal Function ◽  
Maximal Operator ◽  
Variable Exponent ◽  
Differential Operators ◽  
Necessary Condition ◽  
Lebesgue Spaces ◽  
Fractional Maximal Function ◽  
Variable Exponent Lebesgue Spaces ◽  
Bessel Differential Operator

Abstract In this paper, we consider the maximal operator related to the Laplace-Bessel differential operator ( B B -maximal operator) on L p ( ⋅ ) , γ ( R k , + n ) {L}_{p\left(\cdot ),\gamma }\left({{\mathbb{R}}}_{k,+}^{n}) variable exponent Lebesgue spaces. We will give a necessary condition for the boundedness of the B B -maximal operator on variable exponent Lebesgue spaces. Moreover, we will obtain that the B B -maximal operator is not bounded on L p ( ⋅ ) , γ ( R k , + n ) {L}_{p\left(\cdot ),\gamma }\left({{\mathbb{R}}}_{k,+}^{n}) variable exponent Lebesgue spaces in the case of p − = 1 {p}_{-}=1 . We will also prove the boundedness of the fractional maximal function associated with the Laplace-Bessel differential operator (fractional B B -maximal function) on L p ( ⋅ ) , γ ( R k , + n ) {L}_{p\left(\cdot ),\gamma }\left({{\mathbb{R}}}_{k,+}^{n}) variable exponent Lebesgue spaces.

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 A trace inequality for generalized potentials in Lebesgue spaces with variable exponent

2004 ◽  
Vol 2 (1) ◽  
pp. 55-69 ◽  
Author(s):  
David E. Edmunds ◽  
Vakhtang Kokilashvili ◽  
Alexander Meskhi
Keyword(s):  
Variable Exponent ◽  
Homogeneous Type ◽  
Trace Inequality ◽  
Spaces Of Homogeneous Type ◽  
Weighted Inequality ◽  
Euclidean Spaces ◽  
Riesz Potentials ◽  
Lebesgue Spaces ◽  
Fractal Sets

A trace inequality for the generalized Riesz potentialsIα(x)is established in spacesLp(x)defined on spaces of homogeneous type. The results are new even in the case of Euclidean spaces. As a corollary a criterion for a two-weighted inequality in classical Lebesgue spaces for potentialsIα(x)defined on fractal sets is derived.

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