Singular integrals in the rational Dunkl setting

DOI10.1007/s13163-021-00402-1zbMath1504.42036arXiv1910.06433OpenAlexW3184953901WikidataQ114220245 ScholiaQ114220245MaRDI QIDQ2674025

Agnieszka Hejna, Jacek Dziubański

Publication date: 22 September 2022

Published in: Revista Matemática Complutense (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.06433

zbMATH Keywords

singular integralsmaximal functionsDunkl transformsDunkl convolutions

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Linear operators on function spaces (general) (47B38) Integral operators (47G10)

Related Items

Lipschitz and Triebel-Lizorkin spaces, commutators in Dunkl setting, Remarks on Dunkl translations of non-radial kernels, A note on commutators of singular integrals with BMO and VMO functions in the Dunkl setting, Maximal operator, Cotlar's inequality and pointwise convergence for singular integral operators in Dunkl setting

Cites Work

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• Riesz transform and Riesz potentials for Dunkl transform
• Generalized Hermite polynomials and the heat equation for Dunkl operators
• The Dunkl transform
• Reflection groups and orthogonal polynomials on the sphere
• Asymptotic analysis for the Dunkl kernel
• Positivity of Dunkl's intertwining operator
• Dunkl-Schrödinger operators
• Hörmander's multiplier theorem for the Dunkl transform
• Harmonic functions, conjugate harmonic functions and the Hardy space \(H^1\) in the rational Dunkl setting
• Convolution operator and maximal function for the Dunkl transform
• A new mean value property for harmonic functions relative to the Dunkl-Laplacian operator and applications
• Differential-Difference Operators Associated to Reflection Groups
• Integral Kernels with Reflection Group Invariance
• Paley-Wiener Theorems for the Dunkl Transform and Dunkl Translation Operators
• A positive radial product formula for the Dunkl kernel
• Modern Fourier Analysis
• Remark on atomic decompositions for the Hardy space $H^1$ in the rational Dunkl setting