Titchmarsh theorems for Fourier transforms of Hölder-Lipschitz functions on compact homogeneous manifolds

DOI10.1007/s00605-018-1253-0zbMath1418.43002arXiv1702.05731OpenAlexW2599661568MaRDI QIDQ2416326

Julio Delgado, Radouan Daher, Michael Ruzhansky

Publication date: 23 May 2019

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.05731

zbMATH Keywords

Lipschitz functionscompact Lie groupscompact homogeneous manifolds

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Analysis on real and complex Lie groups (22E30) Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. (43A30)

Related Items

Berry-Esseen smoothing inequality for the Wasserstein metric on compact Lie groups ⋮ Asymptotic estimates for the growth of deformed Hankel transform by modulus of continuity ⋮ On the Fourier-Walsh transform of functions from dyadic Dini-Lipschitz classes on the semiaxis ⋮ Generalized Lipschitz conditions for absolute convergence of weighted Jacobi-Dunkl series ⋮ Weighted approximation for the generalized discrete Fourier-Jacobi transform on space \(L_p(\mathbb{T})\) ⋮ Unnamed Item ⋮ Fourier transform of Dini-Lipschitz functions on locally compact Vilenkin groups ⋮ Lipschitz conditions in Damek-Ricci spaces ⋮ Discrete Fourier-Laplace transforms of Lipschitz functions in the spaces \(S^{(p,q)}(\sigma^{m-1})\) ⋮ Characterising extended Lipschitz type conditions with moduli of continuity ⋮ On the Hankel transform of functions from Nikol'ski type classes ⋮ Decay of Fourier Transforms and Generalized Besov Spaces ⋮ Fourier transform of Dini-Lipschitz functions on the field of \(p\)-adic numbers ⋮ On spherical analogues of the classical theorems of Titchmarsh ⋮ On the Fourier transform of functions from the classes \(H_p^\alpha ({{\mathbb{R}}})\) ⋮ Spectral asymptotics at thresholds for a Dirac-type operator on \(\mathbb{Z}^2\) ⋮ Lipschitz and Fourier type conditions with moduli of continuity in rank \(1\) symmetric spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quantization on nilpotent Lie groups
• Characterization of Dini-Lipschitz functions for the Helgason Fourier transform on rank one symmetric spaces
• Fourier transforms of Dini-Lipschitz functions on rank 1 symmetric spaces
• On multipliers on compact Lie groups
• Gevrey functions and ultradistributions on compact Lie groups and homogeneous spaces
• Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups
• Band-limited localized Parseval frames and Besov spaces on compact homogeneous manifolds
• Optimal cubature formulas on compact homogeneous manifolds
• Fourier transforms of Dini-Lipschitz functions
• Fourier multipliers of generalized Lipschitz spaces
• Lipschitz spaces on compact Lie groups
• Absolute convergence of Vilenkin-Fourier series
• Multipliers of Lipschitz spaces on zero dimensional groups
• Multipliers from \(L_ R(\)G) to a Lipschitz-Zygmund class
• Subelliptic estimates and function spaces on nilpotent Lie groups
• Smoothness and absolute convergence of Fourier series in compact totally disconnected groups
• Fourier transforms of Lipschitz functions on certain Lie groups
• The Fourier transforms of Lipschitz functions on certain domains
• The Fourier transforms of Lipschitz functions on the Heisenberg group
• Schatten classes and traces on compact groups
• Lipschitz multipliers on compact O-dimensional groups
• \(L^p\)-nuclearity, traces, and Grothendieck-Lidskii formula on compact Lie groups
• Bernstein-Nikolskii inequalities and Riesz interpolation formula on compact homogeneous manifolds
• \(L^p\) Fourier multipliers on compact Lie groups
• Fourier series of smooth functions on compact Lie groups
• Paley-Wiener-Schwartz nearly Parseval frames on noncompact symmetric spaces
• Nikolskii inequality and Besov, Triebel-Lizorkin, Wiener and Beurling spaces on compact homogeneous manifolds
• Pseudo-Differential Operators and Symmetries
• Estimates for the \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \partial \limits^ - _b $\end{document} complex and analysis on the heisenberg group
• -BOUNDS FOR PSEUDO-DIFFERENTIAL OPERATORS ON COMPACT LIE GROUPS
• Hardy-Littlewood, Hausdorff-Young-Paley inequalities, and L-L Fourier multipliers on compact homogeneous manifolds
• Global Quantization of Pseudo-Differential Operators on Compact Lie Groups, SU(2), 3-sphere, and Homogeneous Spaces
• Fourier Series on Compact Lie Groups