Average Operators on Rectangular Herz Spaces

Espinoza-Villalva, Carolina; Guzmán-Partida, Martha

doi:10.1515/tmmp-2016-0005

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Average Operators on Rectangular Herz Spaces

Tatra Mountains Mathematical Publications

Volume 65 (2016): Issue 1 (March 2016)

By: Carolina Espinoza-Villalva and Martha Guzmán-Partida

Open Access

|Aug 2016

Abstract

We introduce a family of Herz type spaces considering rectangles instead of balls and we study continuity properties of some average operators acting on them.

References

[1] ALVAREZ, J.-GUZMÁN-PARTIDA, M.-LAKEY, J.: Spaces of bounded λ-central mean oscillation, Morrey spaces, and λ-central Carleson measures, Collect. Math. 51 (2000), 1-47.
Search in Google Scholar
[2] BEURLING, A.: Construction and analysis of some convolution algebras, Ann. Inst. Fourier (Grenoble) 14 (1964), 1-32.10.5802/aif.172
Search in Google Scholar
[3] CARTON-LEBRUN, C.-FOSSET, M.: Moyennes et quotients de Taylor dans BMO, Bull. Soc. Roy. Sci. Liège 53 (1984), 85-87.
Search in Google Scholar
[4] CHEN, Y.-LAU, K.: Some new classes of Hardy spaces, J. Funct. Anal. 84 (1989), 255-278.10.1016/0022-1236(89)90097-9
Search in Google Scholar
[5] FEICHTINGER, H.: An elementary approach to Wiener’s third Tauberian theorem on the Euclidean n-space, in: Proc., Conf. at Cortona ’84, Sympos. Math., Vol. 29, Academic Press, New York, 1987, pp. 267-301.
Search in Google Scholar
[6] FEICHTINGER, H.-WEISZ, F.: Herz spaces and summability of Fourier transforms, Math. Nachr. 281 (2008), 309-324.10.1002/mana.200510604
Search in Google Scholar
[7] GARCÍA-CUERVA, J.: Hardy spaces and Beurling algebras, J. London Math. Soc. 39 (1989), 499-513.10.1112/jlms/s2-39.3.499
Search in Google Scholar
[8] HARDY, G.-LITTLEWOOD, J. E.-PÓLYA, G.: Inequalities. Cambridge Univ. Press, Cambridge, 1999.
Search in Google Scholar
[9] HERZ, C.: Lipschitz spaces and Bernstein’s theorem on absolutely convergent Fourier transforms, J. Appl. Math. Mech. 18 (1968), 283-324.
Search in Google Scholar
[10] XIAO, J.: Lp and BMO bounds of weighted Hardy-Littlewood averages, J. Math. Anal. Appl. 262 (2001), 660-666.10.1006/jmaa.2001.7594
Search in Google Scholar
[11] WIENER, N.: Generalized harmonic analysis, Acta Math. 55 (1930), 117-258.10.1007/BF02546511
Search in Google Scholar

DOI: https://doi.org/10.1515/tmmp-2016-0005 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195

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Language: English

Page range: 61 - 70

Submitted on: Jan 1, 2015

Published on: Aug 4, 2016

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

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© 2016 Carolina Espinoza-Villalva, Martha Guzmán-Partida, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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