PARAMETRIC MARCINKIEWICZ INTEGRAL OPERATORS AND COMMUTATORS ON HERZ-HARDY SPACES WITH VARIABLE EXPONENTS

Suping Wang; Guanghui Lu

doi:10.11948/20260037

2027 Volume 17 Issue 1

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Article navigation > Journal of Applied Analysis & Computation > 2027 > 17(1): 145-162

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Suping Wang, Guanghui Lu. PARAMETRIC MARCINKIEWICZ INTEGRAL OPERATORS AND COMMUTATORS ON HERZ-HARDY SPACES WITH VARIABLE EXPONENTS[J]. Journal of Applied Analysis & Computation, 2027, 17(1): 145-162. doi: 10.11948/20260037

Citation:

Suping Wang, Guanghui Lu. PARAMETRIC MARCINKIEWICZ INTEGRAL OPERATORS AND COMMUTATORS ON HERZ-HARDY SPACES WITH VARIABLE EXPONENTS[J]. Journal of Applied Analysis & Computation, 2027, 17(1): 145-162. doi: 10.11948/20260037

PARAMETRIC MARCINKIEWICZ INTEGRAL OPERATORS AND COMMUTATORS ON HERZ-HARDY SPACES WITH VARIABLE EXPONENTS

Suping Wang^1, ,,
Guanghui Lu^2,

1.
School of Mathematics and Information Engineering, Longdong University, Qingyang 745000, China
2.
School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Author Bio: Email: lghwmm1989@126.com(G. Lu)
Corresponding author: Email: ldxyxwc1@163.com(S. Wang)
Fund Project: The authors were supported by National Natural Science Foundation of China Youth Foundation (12201500), Natural Science Foundation of Gansu Province (23JRRM730), Qingyang City Science and Technology Talent Fundation (2025RC1035), the Joint Research Foundation of Qingyang (QYSTK-2024A-069) and Longdong University Doctor Foundation (XYBYZK2112, XYBYZK2113)

Abstract

Abstract

In this paper, the authors obtain the boundedness of parametric Marcinkiewicz integral operator with variable kernel and its commutators on Herz spaces with variable exponents $ \dot{\mathcal{K}}_{p(\cdot)}^{\alpha(\cdot), q(\cdot)}(\mathbb{R}^{n}) $ when the parameters $ \alpha(\cdot), p(\cdot) $ and $ q(\cdot) $ satisfies some conditions. Meanwhile, the corresponding estimates on Herz-Hardy spaces with variable exponents $ H\dot{\mathcal{K}}_{p(\cdot)}^{\alpha(\cdot), q(\cdot)}(\mathbb{R}^{n}) $ are also established.
- Marcinkiewicz integral operators /
- Herz space /
- Herz-Hardy spaces /
- variable exponent /
- commutators
MSC: 42B20, 46E30, 42B35

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References

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