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Behaviour of an oscillatory singular integral on weighted local Hardy spaces

Authors:

Institution:

(1) Department of Economics, Hangszhou University, 310028 Hangzhou, China;(2) Center for Mathematical Sciences, Zhejiang University, 310027 Hangzhou, China

Abstract:

The boundedness on weighted local Hardy spacesh _w ^1,p of the oscillatory singular integral

$Tf(x) = \int_{R^n } {e^{iQ(x,y)} K(x,y)f} (y)dy$

is considered whenQ(x, y)=P(x−y) for some real-valued polynomialP with its degree not less than two. Also a sufficient and necessary condition on polynomialQ onR ⁿ×Rⁿ such thatT mapsh _w ^1,p to the weighted integrable function spaceL _w ¹ is found. This author is partially supported by the National Science Foundation of China and Zhejiang Provincial Sciences Foundation of China

Keywords:

Oscillatory singular integral Weighted local Hardy spaces Muckenhoupt weight Calderon-Zygmund kernel

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