Stability for localized integral operators on weighted spaces of homogeneous type
Corresponding Author
Qiquan Fang
Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou, Zhejiang, P. R. China
Correspondence
Qiquan Fang, Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou, Zhejiang, 310023, P. R. China.
Email: [email protected]
Search for more papers by this authorChang Eon Shin
Department of Mathematics, Sogang University, Seoul, Korea
Search for more papers by this authorXiangxing Tao
Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou, Zhejiang, P. R. China
Search for more papers by this authorCorresponding Author
Qiquan Fang
Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou, Zhejiang, P. R. China
Correspondence
Qiquan Fang, Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou, Zhejiang, 310023, P. R. China.
Email: [email protected]
Search for more papers by this authorChang Eon Shin
Department of Mathematics, Sogang University, Seoul, Korea
Search for more papers by this authorXiangxing Tao
Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou, Zhejiang, P. R. China
Search for more papers by this authorAbstract
Linear operators with off-diagonal decay appear in many areas of mathematics including harmonic and numerical analysis, and their stability is one of the basic assumptions. In this paper, we consider a family of localized integral operators in the Beurling algebra with kernels having mild singularity near the diagonal and certain Hölder continuity property, and prove that their weighted stabilities for different exponents and Muckenhoupt weights are equivalent to each other on a space of homogeneous type with Ahlfors regular measure.
CONFLICT OF INTEREST
The authors declare no potential conflict of interests.
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