3 Generalized almost periodicity in Lebesgue spaces with variable exponents

2021 ◽  
pp. 101-182
Keyword(s):  
Almost Periodicity ◽  
Variable Exponents ◽  
Lebesgue Spaces

scholarly journals Generalized Almost Periodicity in Lebesgue Spaces with Variable Exponents, Part II

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1052
Author(s):  
Marko Kostić ◽  
Wei-Shih Du
Keyword(s):  
Banach Spaces ◽  
Differential Inclusions ◽  
Variable Exponent ◽  
Almost Periodicity ◽  
Variable Exponents ◽  
Almost Periodic ◽  
Fractional Differential Inclusions ◽  
Lebesgue Spaces ◽  
Fractional Differential ◽  
Recurrent Type

In this paper, we introduce and analyze several different notions of almost periodic type functions and uniformly recurrent type functions in Lebesgue spaces with variable exponent L p ( x ) . We primarily consider the Stepanov and Weyl classes of generalized almost periodic type functions and generalized uniformly recurrent type functions. We also investigate the invariance of generalized almost periodicity and generalized uniform recurrence with variable exponents under the actions of convolution products, providing also some illustrative applications to the abstract fractional differential inclusions in Banach spaces.

scholarly journals Generalized Almost Periodicity in Lebesgue Spaces with Variable Exponents

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 928 ◽  
Author(s):  
Marko Kostić ◽  
Wei-Shih Du
Keyword(s):  
Banach Spaces ◽  
Differential Inclusions ◽  
Almost Periodic Functions ◽  
Almost Periodicity ◽  
Variable Exponents ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Lebesgue Spaces ◽  
Recurrent Functions ◽  
Convolution Products

In this paper, we introduce and analyze Stepanov uniformly recurrent functions, Doss uniformly recurrent functions and Doss almost-periodic functions in Lebesgue spaces with variable exponents. We investigate the invariance of these types of generalized almost-periodicity in Lebesgue spaces with variable exponents under the actions of convolution products, providing also some illustrative applications to the abstract semilinear integro-differential inclusions in Banach spaces.

Weak-type inequalities and convergence of the ergodic averages in variable Lebesgue spaces with weights

2009 ◽  
Vol 139 (4) ◽  
pp. 673-683 ◽  
Author(s):  
M. Isabel Aguilar Cañestro ◽  
Pedro Ortega Salvador
Keyword(s):  
Lebesgue Space ◽  
Weak Type ◽  
Suitable Condition ◽  
Variable Exponents ◽  
Ergodic Averages ◽  
Lebesgue Spaces ◽  
Variable Lebesgue Spaces ◽  
Almost Everywhere ◽  
Variable Lebesgue Space ◽  
Measure Preserving Transformation

We characterize the weighted weak-type inequalities with variable exponents for the maximal operator associated with an ergodic, invertible, measure-preserving transformation and prove the almost everywhere convergence of the ergodic averages for all functions in a variable Lebesgue space with a weight verifying a suitable condition.

scholarly journals Boundedness of multilinear Calderón-Zygmund singular operators on weighted Lebesgue spaces and Morrey-Herz spaces with variable exponents

2021 ◽  
Vol 6 (10) ◽  
pp. 11246-11262
Author(s):  
Yueping Zhu ◽  
◽  
Yan Tang ◽  
Lixin Jiang ◽  
Keyword(s):  
Variable Exponent ◽  
Variable Exponents ◽  
Herz Spaces ◽  
Lebesgue Spaces ◽  
Singular Operators ◽  
Weighted Lebesgue Spaces

<abstract><p>In this paper, we introduce weighted Morrey-Herz spaces $ M\dot K^{\alpha, \lambda}_{q, p(\cdot)}(w~^{p(\cdot)}) $ with variable exponent $ p(\cdot) $. Then we prove the boundedness of multilinear Calderón-Zygmund singular operators on weighted Lebesgue spaces and weighted Morrey-Herz spaces with variable exponents.</p></abstract>

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