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 : email@example.com Young Ja PARK Department of Mathematics, Hoseo University, Hoeo-ro 79, Asan-si, Chungnam, 31499,Republicof Korea E-mail : firstname.lastname@example.org 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 . In order that a function space can be applied to diverse realms, it
Acta Mathematica Sinica, English Series – Springer Journals
Published: May 28, 2018
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