Analysis on harmonic extensions of H-type groups

2015/03/18 by Maria Vallarino, Vallarino, Maria · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1504.00329

Abstract

The subject of this PhD thesis is harmonic analysis on solvable extensions of H-type groups. Let N be an H-type group and S=NA be its solvable extension of rank one. The author study the weak type 1 boundedness of suitable Hardy-Littlewood maximal functions on S and develop a Calderon-Zygmund theory on S. The previous theory is then applied to obtain a Mihlin-Hormander type theorem for spectral multipliers of a distinguished Laplacian on S.

Citations

• Hp spaces of several variables

Cited by

• Titchmarsh theorems, Hausdorff-Young-Paley inequality and L^p-L^q\n boundedness of Fourier multipliers on harmonic NA groups

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