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Author: Feng, Han Item type: Thesis

  • Spherical h-Harmonic Analysis and Related Topics

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    Spring 2016

    Feng, Han

    This thesis contains the following three parts: \egin{description} \item[Part 1(Chapters 1-5):] Spherical $h$-harmonic analysis. \item[Part 2:] Reverse H\"{o}lder's inequality for spherical harmonics. \item[Part 3:] Multivariate Lagrange and Hermite approximation and pointwise limits...

  • Weighted Hardy-Littlewood-Sobolev Inequality on the Unit Sphere

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    Fall 2013

    Feng, Han

    One of the main aims in this thesis is to establish analogues of the classical Hardy-Littlewood-Sobolev (HLS) inequality for weighted orthogonal polynomial expansions (WOPEs) on the unit sphere, the unit ball and the simplex. An optimal condition for which this inequality holds is obtained....

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