Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 505-522

SINGULAR INTEGRAL OPERATORS WITH ROUGH KERNELS ON CENTRAL MORREY SPACES WITH VARIABLE EXPONENT

Zunwei Fu, Shanzhen Lu, Hongbin Wang and Liguang Wang

The University of Suwon, Department of Computer Science
Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do, 445-743, Korea
and Qufu Normal University, School of Mathematical Sciences
Qufu, Shandong, 273100, P.R. China; zwfu 'at' mail.bnu.edu.cn, zwfu 'at' suwon.ac.kr

Beijing Normal University, School of Mathematical Sciences
Beijing, 100875, P.R. China; lusz 'at' bnu.edu.cn

Shandong University of Technology, School of Mathematics and Statistics
Zibo, Shandong, 255049, P.R. China;
and University of Chinese Academy of Sciences, School of Mathematical Sciences
Beijing, 100049, P.R. China; hbwang 'at' ucas.ac.cn

Qufu Normal University, School of Mathematical Sciences
Qufu, Shandong, 273100, P.R. China; wangliguang0510 'at' 163.com

Abstract. In this paper we define the λ-central BMO spaces and the central Morrey spaces with variable exponent. We obtain the boundedness of the singular integral operator T_Ω,α and its commutator [b,T_Ω,α] on central Morrey spaces with variable exponent, where Ω &isin: L^s(S^n-1) for s ≥ 1 be homogeneous function of degree zero, 0 ≤ α < n and b be λ-central BMO functions. As applications, we consider the regularity in the central Morrey spaces with variable exponent of strong solutions to nondivergence elliptic equations with VMO coefficients.

2010 Mathematics Subject Classification: Primary 42B35, 42B20, 46E30.

Key words: λ-central BMO spaces, central Morrey space, variable exponent, commutator, singular integral operator.

Reference to this article: Z. Fu, S. Lu, H. Wang and L. Wang: Singular integral operators with rough kernels on central Morrey spaces with variable exponent. Ann. Acad. Sci. Fenn. Math. 44 (2019), 505-522.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4431