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Calderón‐Zygmund operators with non‐diagonal singularity
Author(s) -
Li Kangwei,
Sun Wenchang
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200338
Subject(s) - mathematics , diagonal , singular integral operators , singularity , singular integral operators of convolution type , kernel (algebra) , type (biology) , pure mathematics , fourier integral operator , class (philosophy) , operator theory , singular integral , mathematical analysis , algebra over a field , microlocal analysis , integral equation , geometry , ecology , artificial intelligence , computer science , biology
In this paper, we introduce a class of singular integral operators which generalize Calderón‐Zygmund operators to the more general case, where the set of singular points of the kernel need not to be the diagonal, but instead, it can be a general hyper curve. We show that such operators have similar properties as ordinary Calderón‐Zygmund operators. In particular, we prove that they are of weak‐type (1, 1) and strong type ( p , p ) for 1 < p < ∞ .