Radial mollifiers, mean value operators and harmonic functions in Dunkl theory

DOI10.1016/j.jmaa.2016.10.049zbMath1360.31007OpenAlexW2541939527MaRDI QIDQ342948

Léonard Gallardo, Chaabane Rejeb

Publication date: 18 November 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2016.10.049

zbMATH Keywords

Dunkl convolution productDunkl harmonic functionsDunkl-Laplacian operatorgeneralized volume mean value operator

Mathematics Subject Classification ID

Homomorphisms and multipliers of function spaces on groups, semigroups, etc. (43A22) Harmonic, subharmonic, superharmonic functions on other spaces (31C05)

Related Items (3)

Newtonian potentials and subharmonic functions associated to root systems ⋮ Boundedness of bilinear Dunkl–Hausdorff operators on products of Lebesgue and Morrey spaces ⋮ Green function and Poisson kernel associated to root systems for annular regions

Cites Work

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• A transference theorem for the Dunkl transform and its applications
• The Dunkl transform
• Positivity of Dunkl's intertwining operator
• A uniform proof of the Macdonald-Mehta-Opdam identity for finite Coxeter groups
• Harmonic Function Theory
• A new mean value property for harmonic functions relative to the Dunkl-Laplacian operator and applications
• Differential-Difference Operators Associated to Reflection Groups
• On a mean value property associated with the dunkl laplacian operator and applications
• The dunkel intertwining operator on spaces of functions and distributions and integral representation of its dual
• Paley-Wiener Theorems for the Dunkl Transform and Dunkl Translation Operators
• A positive radial product formula for the Dunkl kernel
• On the boundedness of the Dunkl spherical maximal operator

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