Weakly Strongly Singular Integral Operators on Anisotropic Hardy Spaces and Their Dual Operators
Weakly Strongly Singular Integral Operators on Anisotropic Hardy Spaces and Their Dual Operators
摘要
Let A be an expansive dilation. We define weakly strongly singular integral kernels and study the action of the operators induced by these kernels on anisotropic Hardy spaces associated with A.
Let A be an expansive dilation. We define weakly strongly singular integral kernels and study the action of the operators induced by these kernels on anisotropic Hardy spaces associated with A.
基金
supported by NSF of China (Grant No.10571015)
RFDP of China (Grant No.20050027025)
NSF of Zhejiang Province (Grant No.Y7080325)
参考文献13
-
1Hirschmann, I. I.: On multiplier transformations. Duke Math. J., 26, 222-242 (1959).
-
2Wainger, S.: Special trigonometric series in k dimensions. Mem. Amer. Math. Soc.,59 (1965).
-
3Fefferman, C.: Inequalities for strongly singular convolution operators. Acta Math., 124, 9-36 (1970).
-
4Fefferman, C., Stein, E. M.: HP spaces of several variables. Acta Math., 129, 137-193 (1972).
-
5Bjork, J. E.: Lp estimates for convolution operators defined by compactly supported distributions in R^n Math. Scand., 34, 129-136 (1974).
-
6Sjolin, P.: Lp estimates for strongly singular convolution operators in R^n. Ark. Math., 14, 59-64 (1976).
-
7Coifman, R. R.: A real variable characterization of Hp. Studia Math., 51, 269 -274 (1974).
-
8Bordin, B.: HP estimates for weakly strongly singular integral operators on spaces of homogeneous type Studia Math., 75, 217-234 (1983).
-
9Bownik, M.: Anisotropic Hardy spaces and wavelets. Mere. Amer. Math. Soc., 164(781), 122 (2003).
-
10Calderon, A. P., Torchinsky, A.: Parabolic maximal functions associated with a distribution. Advances in Math., 16, 1-64 (1975).
-
1Jun Feng LI.The Estimates for Sharp Maximal Functions of Multilinear Strongly Singular Integral Operators[J].Acta Mathematica Sinica,English Series,2005,21(6):1495-1508.
-
2Jun Feng LI,Shan Zhen LU.Strongly Singular Integral Operators on Weighted Hardy Space[J].Acta Mathematica Sinica,English Series,2006,22(3):767-772. 被引量：6
-
3LIJunfeng LUShanzhen.The boundedness of multilinear operators of strongly singular integral operators on Hardy spaces[J].Progress in Natural Science:Materials International,2005,15(1):10-16. 被引量：1
-
4黄文礼,陶祥兴,李胜宏.Weighted estimates for strongly singular integral operators with rough kernels[J].Applied Mathematics and Mechanics(English Edition),2010,31(6):761-768.
