HERMITE EXPANSIONS AND FRACTAL MEASURES

数学物理学报(英文版) ›› 1998, Vol. 18 ›› Issue (2): 167-173.

HERMITE EXPANSIONS AND FRACTAL MEASURES

张震球

Department of Mathematics, Tianjin University, Tianjin 300072, China

收稿日期:1996-03-27 修回日期:1996-05-20 出版日期:1998-06-25 发布日期:1998-06-25

HERMITE EXPANSIONS AND FRACTAL MEASURES

Zhang Zhenqiu

Department of Mathematics, Tianjin University, Tianjin 300072, China

Received:1996-03-27 Revised:1996-05-20 Online:1998-06-25 Published:1998-06-25

摘要/Abstract

摘要： Let μ be a locally uniformly α-dimensioual measure on Rⁿ and P_t(fdμ) be the Able Poisson means of Hermite expansions for f∈L^P(dμ), it is studied that the asymptotis properties of P_t(fdμ) as t→1_. Analogue of Wiener's theorem is obtained.Author also establishs the boundedness of the α-dimensional maximal conjugate Poisson integral operators from L^P(dμ) to the Lebesgue p-power integrable function spaces L^P(dx),and this derives directly the boundedness of Riesz transforms.

关键词: Fractal measurest Hermite expansions, Riesz transforms

Abstract: Let μ be a locally uniformly α-dimensioual measure on Rⁿ and P_t(fdμ) be the Able Poisson means of Hermite expansions for f∈L^P(dμ), it is studied that the asymptotis properties of P_t(fdμ) as t→1_. Analogue of Wiener's theorem is obtained.Author also establishs the boundedness of the α-dimensional maximal conjugate Poisson integral operators from L^P(dμ) to the Lebesgue p-power integrable function spaces L^P(dx),and this derives directly the boundedness of Riesz transforms.

Key words: Fractal measurest Hermite expansions, Riesz transforms

张震球. HERMITE EXPANSIONS AND FRACTAL MEASURES[J]. 数学物理学报(英文版), 1998, 18(2): 167-173.

Zhang Zhenqiu. HERMITE EXPANSIONS AND FRACTAL MEASURES[J]. Acta mathematica scientia,Series B, 1998, 18(2): 167-173.

[1]	J.J. Betancor, R. Crescimbeni, J.L. Torrea. OSCILLATION AND VARIATION OF THE LAGUERRE HEAT AND POISSON SEMIGROUPS AND RIESZ TRANSFORMS[J]. 数学物理学报(英文版), 2012, 32(3): 907-928.
[2]	李澎涛, 彭立中. L^p BOUNDEDNESS OF COMMUTATOR OPERATOR ASSOCIATED WITH SCHRÖDINGER OPERATORS ON HEISENBERG GROUP[J]. 数学物理学报(英文版), 2012, 32(2): 568-578.

HERMITE EXPANSIONS AND FRACTAL MEASURES

HERMITE EXPANSIONS AND FRACTAL MEASURES

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