| 研究概要 |
(1)Singular integral, Hardy space, Rough kernel, Fractional integral, by D.Fan and S.Sato (改訂版)
Abstract : We study the singular integrals associated with the variable surfaces of revolution. We treat the rough kernel case where the singular integral is defined by an H^1 kernel function on the sphere S^{n-1}. We prove the L^p boundedness of the singular integral for p greater than 1 and less than or equal to 2,assuming that a certain lower dimensional maximal operator is bounded on L^s for all s>1. We also study the (L^p, L^r) boundedness for the fractional integrals associated with the surfaces of revolution.
(変化する回転面に付随したある種の特異積分およびfractional integralを考えて,それらのL^p-L^q有界性考察した.特異積分の有界性を示す際には積分核の斉次部分にはH^1条件とcancellation条件を仮定する.また,この特異積分に付随したある種の最大関数のL^p有界性を仮定する.証明には単位球面上のHardy空間に対するアトム分解を用いる.)
(2)Weighted weak type (1,1) estimates for singular integrals and Littlewood-Paley functions, by D.Fan and S.sato (to appear in Studia Math.)
Abstract : We prove some weighted weak type (1,1) inequalities for certain singular integrals and Littlewood-Paley functions. We study the rough kernel cases.
(3)A note on weighted estimates for certain classes of pseudo-differential operators, by S.Sato (to appear in Rocky Mountain J. Math.)
Abstract : We consider certain classes of pseudo-differential operators and prove the L^2_w-L^2_w estimates, L^1_w-weak L^1_w estimates and H^1_w-L^1_w estimates.
(4)特異積分とLittlewood-Paley関数,佐藤秀一,数学(岩波書店),第55巻第2号,2003年4月春季号,128-147 内容:論説.
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