On rough generalized Marcinkiewicz integrals along surfaces of revolution on product spaces-Reference-Cited by-同舟云学术

On rough generalized Marcinkiewicz integrals along surfaces of revolution on product spaces

Published:2024 Issue:2 Volume:9 Page:4816-4829
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Ali Mohammed¹,Al-Qassem Hussain²

Affiliation:

1. Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan

2. Mathematics Program, Department of Mathematics, Statistics and Physics, College of Arts and Sciences, Qatar University, 2713, Doha, Qatar

Abstract

<abstract><p>In this paper, we prove the $ L^p $ boundedness of generalized Marcinkiewicz operators along surfaces of revolution on product spaces under very weak conditions on the the singular kernels. Our results generalize and improve many previously known results.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference34 articles.

1. A. Benedek, A. Calderón, R. Panzones, Convolution operators on Banach space valued functions, Proc. Natl. Acad. Sci., 48 (1962), 356–365. https://doi.org/10.1073/pnas.48.3.356

2. Y. Ding, D. Fan, Y. Pan, $L^p$ boundedness of Marcinkiewicz integrals with Hardy space function kernel, Acta Math., 16 (2000), 593–600. https://doi.org/10.1007/s101140000015

3. H. Wu, $L^p$ bounds for Marcinkiewicz integrals associated to surfaces of revolution, J. Math. Anal. Appl., 321 (2006), 811–827. https://doi.org/10.1016/j.jmaa.2005.08.087

4. Y. Ding, D. Fan, Y. Pan, On the $L^p$ boundedness of Marcinkiewicz integrals, Mich. Math. J., 50 (2002), 17–26. https://doi.org/10.1307/mmj/1022636747

5. F. Liu, A note on Marcinkiewicz integrals associated to surfaces of revolution, J. Aust. Math. Soc., 104 (2018), 380–402. https://doi.org/10.1017/S1446788717000143