Spectrum and Singular Integrals on a New Weighted Function Space

Spectrum and Singular Integrals on a New Weighted Function Space Acta Mathematica Sinica, English Series Acta Mathematica Sinica, Published online: May 28, 2018 https://doi.org/10.1007/s10114-018-7043-8 English Series http://www.ActaMath.com Springer-Verlag GmbH Germany & The Editorial Office of AMS 2018 1) Hee Chul PAK Department of Mathematics, Dankook University, Dandae-ro 119, Dongnam-gu, Cheonan-si, Chungnam, 31116,Republicof Korea E-mail : hpak@dankook.ac.kr Young Ja PARK Department of Mathematics, Hoseo University, Hoeo-ro 79, Asan-si, Chungnam, 31499,Republicof Korea E-mail : ypark@hoseo.edu Abstract We introduce a new function space that is much finer than the classical Lebesgue spaces, and investigate the continuity and the discontinuity of the Calder´ on–Zygmund operators on the new weighted spaces. In order to identify the continuity of singular integrals, we prove an interpolation theorem on the new spaces and propose a concept of the spectrum of base functions. Keywords Function spaces, singular integrals, interpolation, Calder´ on–Zygmund operators, H¨ older’s inequality, L log L MR(2010) Subject Classification 46E30, 32A55, 42B20, 42B25, 41A05, 46B70 1 Introduction We have built up a new function space in order to generalize the classical Lebesgue spaces, and to find an appropriate space covering solutions of elliptic partial differential equations equipped with more universal flux terms [4]. In order that a function space can be applied to diverse realms, it http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematica Sinica, English Series Springer Journals

Spectrum and Singular Integrals on a New Weighted Function Space

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
1439-8516
eISSN
1439-7617
D.O.I.
10.1007/s10114-018-7043-8
Publisher site
See Article on Publisher Site

Abstract

Acta Mathematica Sinica, English Series Acta Mathematica Sinica, Published online: May 28, 2018 https://doi.org/10.1007/s10114-018-7043-8 English Series http://www.ActaMath.com Springer-Verlag GmbH Germany & The Editorial Office of AMS 2018 1) Hee Chul PAK Department of Mathematics, Dankook University, Dandae-ro 119, Dongnam-gu, Cheonan-si, Chungnam, 31116,Republicof Korea E-mail : hpak@dankook.ac.kr Young Ja PARK Department of Mathematics, Hoseo University, Hoeo-ro 79, Asan-si, Chungnam, 31499,Republicof Korea E-mail : ypark@hoseo.edu Abstract We introduce a new function space that is much finer than the classical Lebesgue spaces, and investigate the continuity and the discontinuity of the Calder´ on–Zygmund operators on the new weighted spaces. In order to identify the continuity of singular integrals, we prove an interpolation theorem on the new spaces and propose a concept of the spectrum of base functions. Keywords Function spaces, singular integrals, interpolation, Calder´ on–Zygmund operators, H¨ older’s inequality, L log L MR(2010) Subject Classification 46E30, 32A55, 42B20, 42B25, 41A05, 46B70 1 Introduction We have built up a new function space in order to generalize the classical Lebesgue spaces, and to find an appropriate space covering solutions of elliptic partial differential equations equipped with more universal flux terms [4]. In order that a function space can be applied to diverse realms, it

Journal

Acta Mathematica Sinica, English SeriesSpringer Journals

Published: May 28, 2018

References

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