scholarly journals Linear Methods for Summing Fourier Series and Approximation Properties of Fourier Series in Weighted Lebesgue Spaces with Variable Exponent

2021 ◽  
Author(s):  
Ahmet TESTİCİ ◽  
Daniyal M. İSRAFİLZADE
Keyword(s):  
Fourier Series ◽  
Variable Exponent ◽  
Approximation Properties ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces

scholarly journals Approximation theorems in weighted Lebesgue spaces with variable exponent

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 561-577
Author(s):  
Ahmet Testici
Keyword(s):  
Weight Function ◽  
Approximation Theory ◽  
Variable Exponent ◽  
Approximation Properties ◽  
Lebesgue Spaces ◽  
Approximation Theorems ◽  
Weighted Lebesgue Spaces ◽  
Muckenhoupt Class

In this work, approximation properties of de la Vall?e-Poussin means are investigated in weighted Lebesgue spaces with variable exponent where weight function belongs to Muckenhoupt class. For this purpose direct, inverse and simultaneous theorems of approximation theory are proved and constructive characterizations of functions are obtained in weighted Lebesgue spaces with variable exponent.

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

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>

Singular Integrals in Weighted Lebesgue Spaces with Variable Exponent

2003 ◽  
Vol 10 (1) ◽  
pp. 145-156 ◽  
Author(s):  
V. Kokilashvili ◽  
S. Samko
Keyword(s):  
Lebesgue Space ◽  
Variable Exponent ◽  
Weighted Space ◽  
Singular Integrals ◽  
Power Weight ◽  
Weighted Lebesgue Space ◽  
Lebesgue Spaces ◽  
Dini Condition ◽  
Zygmund Operator ◽  
Weighted Lebesgue Spaces

Abstract In the weighted Lebesgue space with variable exponent the boundedness of the Calderón–Zygmund operator is established. The variable exponent 𝑝(𝑥) is assumed to satisfy the logarithmic Dini condition and the exponent β of the power weight ρ(𝑥) = |𝑥 – 𝑥0| β is related only to the value 𝑝(𝑥0). The mapping properties of Cauchy singular integrals defined on the Lyapunov curve and on curves of bounded rotation are also investigated within the framework of the above-mentioned weighted space.

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.

Sign in / Sign up

Export Citation Format

Share Document