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>

scholarly journals Boundedness of vector-valued sublinear operators on weighted Herz-Morrey spaces with variable exponents

2021 ◽  
Vol 19 (1) ◽  
pp. 412-426
Author(s):  
Shengrong Wang ◽  
Jingshi Xu
Keyword(s):  
Variable Exponent ◽  
Morrey Spaces ◽  
Variable Exponents ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces ◽  
Sublinear Operators ◽  
Size Condition ◽  
Vector Valued

Abstract If vector-valued sublinear operators satisfy the size condition and the vector-valued inequality on weighted Lebesgue spaces with variable exponent, then we obtain their boundedness on weighted Herz-Morrey spaces with variable exponents.

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.

The Chen-Marchaud fractional integro-differentiation in the variable exponent Lebesgue spaces

2011 ◽  
Vol 14 (3) ◽  
Author(s):  
Humberto Rafeiro ◽  
Makhmadiyor Yakhshiboev
Keyword(s):  
Integral Operator ◽  
Fractional Derivative ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Inverse Operator ◽  
Fractional Integral Operator ◽  
Left Inverse ◽  
Fractional Differentiation ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces

AbstractAfter recalling some definitions regarding the Chen fractional integro-differentiation and discussing the pro et contra of various ways of truncation related to Chen fractional differentiation, we show that, within the framework of weighted Lebesgue spaces with variable exponent, the Chen-Marchaud fractional derivative is the left inverse operator for the Chen fractional integral operator.

scholarly journals Wavelet characterization of local Muckenhoupt weighted Lebesgue spaces with variable exponent

2020 ◽  
Vol 198 ◽  
pp. 111930
Author(s):  
Mitsuo Izuki ◽  
Toru Nogayama ◽  
Takahiro Noi ◽  
Yoshihiro Sawano
Keyword(s):  
Variable Exponent ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces
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