Analysis on harmonic extensions of H-type groups

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.

Cited by in corpus (4)

• Spectral multipliers for sub-Laplacians on solvable extensions of stratified groups
• Riesz transforms on solvable extensions of stratified groups
• Equivalent Characterizations for Boundedness of Maximal Singular Integrals on $ax+b$\,--Groups
• Titchmarsh theorems, Hausdorff-Young-Paley inequality and $L^p$-$L^q$ boundedness of Fourier multipliers on harmonic $NA$ groups