Acta mathematica scientia,Series B ›› 1998, Vol. 18 ›› Issue (2): 167-173.
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Zhang Zhenqiu
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Abstract: Let μ be a locally uniformly α-dimensioual measure on Rn and Pt(fdμ) be the Able Poisson means of Hermite expansions for f∈LP(dμ), it is studied that the asymptotis properties of Pt(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 LP(dμ) to the Lebesgue p-power integrable function spaces LP(dx),and this derives directly the boundedness of Riesz transforms.
Key words: Fractal measurest Hermite expansions, Riesz transforms
Zhang Zhenqiu. HERMITE EXPANSIONS AND FRACTAL MEASURES[J].Acta mathematica scientia,Series B, 1998, 18(2): 167-173.
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