2004•Journal of Zhejiang University(Sciences Edition)Requires access
Boundedness of sigular integral operator on Herz type space.
Yanmei Di
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Abstract
The sigular integral operator T_(Ω,β)f(x)=p.v.∫_(R~n)b(|y|)Ω(y′)|y|~(-n-β)f(x-y)dy defined on all-test function f is studied, where b is a bounded function, β≥0,Ω(y′) is an integrable function on unit sphere S~(n-1) satisfying certain cancellation conditions. It is proved that, for 0αn1-1q,1q∞,0p∞,T_(Ω,β)(extends) to be a bounded operator from the Herz type Sobolev space to Herz type space with Ω being a distribution in the Hardy space H~r(S~(n-1)) with r=n-1n-1+β.