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The main result is a Paleys theory for lacunary Fourier series using semigroup-BMO and $H^1$ spaces. This interpretation allows an extension of Paleys theory to general discrete groups, complementing the work of Rudin for abelian groups with a total order, and Lust-Piquard and Pisiers work for lacunary Fourier series with operator-valued coefficients.
This article studies Paleys theory for lacunary Fourier series on (nonabelian) discrete groups. The results unify and generalize the work of Rudin for abelian discrete groups and the work of Lust-Piquard and Pisier for operator valued functions, an
Let $G$ be a compact group. For $1leq pleqinfty$ we introduce a class of Banach function algebras $mathrm{A}^p(G)$ on $G$ which are the Fourier algebras in the case $p=1$, and for $p=2$ are certain algebras discovered in cite{forrestss1}. In the case
We investigate Beurling-Fourier algebras, a weighted version of Fourier algebras, on various Lie groups focusing on their spectral analysis. We will introduce a refined general definition of weights on the dual of locally compact groups and their ass
Let $G$ be a compact connected Lie group. The question of when a weighted Fourier algebra on $G$ is completely isomorphic to an operator algebra will be investigated in this paper. We will demonstrate that the dimension of the group plays an importan
We prove that the negative infinitesimal generator $L$ of a semigroup of positive contractions on $L^infty$ has a bounded $H^infty(S_eta^0)$-calculus on the associated Poisson semigroup-BMO space for any angle $eta>pi/2$, provided the semigroup satis