Estimates for functions of generalized Marcinkiewicz operators related to surfaces of revolution-Reference-Cited by-同舟云学术

Estimates for functions of generalized Marcinkiewicz operators related to surfaces of revolution

Published:2024 Issue:8 Volume:9 Page:22287-22300
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Ali Mohammed¹,Katatbeh Qutaibeh¹,Al-Refai Oqlah²,Al-Shutnawi Basma³

Affiliation:

1. Department of Mathematics and Statistics, Faculty of Science and Arts, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan

2. Department of Mathematics, Faculty of Science, Zarqa University, P.O.Box 132222, Zarqa 13132, Jordan

3. Department of mathematics, Faculty of Science, Tafila Technical University, P.O. Box 179, Tafila 66110, Jordan

Abstract

<p>In this paper, specific $ L^p $ estimates for generalized Marcinkiewicz operators correlated to surfaces of revolution are proved. These estimates and the extrapolation procedure of Yano are employed to confirm the $ L^p $ boundedness of the above-mentioned integrals under weaker assumptions on the singular kernels. Our findings generalize and improve several known results.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference25 articles.

1. E. Stein, On the functions of Littlewood-Paley, Lusin and Marcinkiewicz, Trans. Amer. Math. Soc., 88 (1958), 430–466. https://doi.org/10.1090/S0002-9947-1958-0112932-2

2. T. Walsh, On the function of Marcinkiewicz, Stud. Math., 44 (1972), 203–217. https://doi.org/10.4064/sm-44-3-203-217

3. A. Al-Salman, H. Al-Qassem, L. Cheng, Y. Pan, $L^p$ bounds for the function of Marcinkiewicz, Math. Res. Lett., 9 (2002), 697–700. http://dx.doi.org/10.4310/MRL.2002.v9.n5.a11

4. H. M. Al-Qassem, A. J. Al-Salman, A note on Marcinkiewicz integral operators, J. Math. Anal. Appl., 282 (2003), 698–710. https://doi.org/10.1016/S0022-247X(03)00244-0

5. H. Al-Qassem, A. Al-Salman, Rough Marcinkiewicz integrals related to surfaces of revolution, Asian J. Math., 7 (2003), 219–230. http://dx.doi.org/10.4310/AJM.2003.v7.n2.a4