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The boundedness of singular integral operator along an open curve
Authors:Wang Xiaolin  Min Honglin
Affiliation:(1) College of Mathematical Sciences, Wuhan University, 430072 Wuhan, China
Abstract:It is well known that, the singular integral operatorS defined as: 
$$left( {Svarphi } right)left( {t_0 } right) = frac{1}{{pi i}}int {_L frac{{varphi left( t right)}}{{t - t_0 }}} dt left( {t_0  in L} right)$$
ifL is a closed smooth contour in the complex plane C, thenS is a bounded linear operator fromH μ(L) intoH μ(L): ifL is an open smooth curve, thenS is just a linear operator fromH * intoH *. In this paper, we define a Banach space 
$$H_{lambda _1 , lambda _2 }^mu  $$
, and prove that 
$$S:H_{lambda _1 , lambda _2 }^mu   to H_{lambda _1 , lambda _2 }^mu  $$
is a bounded linear operator, then verify the boundedness of other kinds of singular integral operators. Supported by the National Science Foundation of China Wang Xiaolin: born in Aug. 1950, Professor
Keywords:singular integral operator     IE4"  >   /content/151R1J73N4528313/11859_2008_Article_BF02830033_TeX2GIFIE4.gif"   alt="     $$H_{lambda _1 , lambda _2 }^mu $$   "   align="  middle"   border="  0"  > space  boundedness
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