ORIGINAL PAPER

Strong maximal operator and singular integral operators in weighted Morrey spaces on product domains

Corresponding Author

Kwok-Pun Ho

[email protected]

Department of Mathematics and Information Technology, The Hong Kong Institute of Education, 10 Lo Ping Road, Tai Po, Hong Kong, China

e-mail: [email protected], Phone: +852 29488386, Fax: +852 29487726Search for more papers by this author

Kwok-Pun Ho,

Corresponding Author

Kwok-Pun Ho

[email protected]

Department of Mathematics and Information Technology, The Hong Kong Institute of Education, 10 Lo Ping Road, Tai Po, Hong Kong, China

e-mail: [email protected], Phone: +852 29488386, Fax: +852 29487726Search for more papers by this author

First published: 19 December 2016

https://doi.org/10.1002/mana.201500429

Citations: 6

Share a link

Email
Wechat
Bluesky

Abstract

We introduce the Morrey spaces on product domains and extend the boundedness of strong maximal operator and singular integral operators on product domains to Morrey spaces.

References

1D. Adams, A note on Riesz potentials, Duke Math. J. 42(4), 765–778 (1975).
10.1215/S0012-7094-75-04265-9
Web of Science® Google Scholar
2J. Alvarez, On the T(1) theorem on product domains, J. Anal. Math. 62, 155–167 (1994).
10.1007/BF02835952
Web of Science® Google Scholar
3S.-Y. Chang and R. Fefferman, Some recent developments in Fourier analysis and $urn:x-wiley:0025584X:media:mana201500429:mana201500429-math-0330$ -theory on product domain, Bull. Amer. Math. Soc. 12, 1–43 (1985).
10.1090/S0273-0979-1985-15291-7
Web of Science® Google Scholar
4F. Chiarenza and M. Frasca, Morrey Spaces and Hardy–Littlewood maximal function, Rend. Mat. Appl. (7) 7, 273–279 (1987).
Google Scholar
5R. Fefferman, Harmonic analysis on product spaces, Ann. of Math. 126, 109–130 (1987).
10.2307/1971346
Web of Science® Google Scholar
6R. Fefferman and E. Stein, Singular integrals on product spaces, Adv. Math. 45, 117–143 (1982).
10.1016/S0001-8708(82)80001-7
Web of Science® Google Scholar
7J. García-Cuerva and J. Rubio de Francia, Weighted Norm Inequalities and Related Topics (North-Holland, 1985).
Google Scholar
8L. Grafakos, Modern Fourier Analysis, 2^nd ed. (Springer, 2008).
Google Scholar
9K.-P. Ho, Vector-valued singular integral operators on Morrey type spaces and variable Triebel–Lizorkin-Morrey spaces, Ann. Acad. Sci. Fenn. Math. 37, 375–406 (2012).
10.5186/aasfm.2012.3746
Web of Science® Google Scholar
10K.-P. Ho, Atomic decompositions of weighted Hardy–Morrey spaces, Hokkaido Math. J. 42, 131–157 (2013).
10.14492/hokmj/1362406643
Web of Science® Google Scholar
11K.-P. Ho, Vector-valued operators with singular kernel and Triebel–Lizorkin-block spaces with variable exponents, Kyoto J. Math. 56, 97–124 (2016).
10.1215/21562261-3445165
Web of Science® Google Scholar
12B. Jessen, J. Marcinkiewicz, and A. Zygmund, Note on the differentiability of multiple integrals, Fund. Math. 25, 217–234 (1935).
10.4064/fm-25-1-217-234
Google Scholar
13J.-L. Journé, Calderón–Zygmund operators on product spaces, Rev. Mat. Iberoamer. 1, 55–91 (1985).
10.4171/RMI/15
Google Scholar
14Y. Komori and S. Shirai, Weighted Morrey spaces and a singular integral operator, Math. Nachr. 282, 219–231 (2009).
10.1002/mana.200610733
Web of Science® Google Scholar
15S. Lu, D. Yang, and G. Hu, Herz Type Spaces and their Applications (Science Press, Beijing, 2008).
Google Scholar
16T. Mizuhara, Boundedness of some classical operators on generalized Morrey spaces, In Harmonic Analysis, ICM 90 Satellite Procedings (Springer-Verlag, 1991), pp. 183–189.
Google Scholar
17C. Morrey, On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc. 43, 126–166 (1938).
10.1090/S0002-9947-1938-1501936-8
Web of Science® Google Scholar
18E. Nakai, Hardy–Littlewood maximal operator, singular integral operators and the Riesz potentials on generalized Morrey spaces, Math. Nachr. 166, 95–104 (1994).
10.1002/mana.19941660108
Web of Science® Google Scholar

Citing Literature

Volume290, Issue16

November 2017

Pages 2629-2640

Strong maximal operator and singular integral operators in weighted Morrey spaces on product domains

Abstract

References

Citing Literature

References

Information

About Wiley Online Library

Help & Support

Opportunities

Connect with Wiley

Strong maximal operator and singular integral operators in weighted Morrey spaces on product domains

Abstract

References

Citing Literature

References

Related

Information