Harmonic functions, conjugate harmonic functions and the Hardy space \(H^1\) in the rational Dunkl setting

DOI10.1007/s00041-019-09666-0zbMath1426.42017arXiv1802.06607OpenAlexW2964117608MaRDI QIDQ2326867

Agnieszka Hejna, Jacek Dziubański, Jean-Philippe Anker

Publication date: 10 October 2019

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

Full work available at URL: https://arxiv.org/abs/1802.06607

zbMATH Keywords

maximal operatorsHardy spacesRiesz transformsCauchy-Riemann equationsrational Dunkl theory

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Function spaces arising in harmonic analysis (42B35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) (H^p)-spaces (42B30) Orthogonal polynomials and functions associated with root systems (33C52) Heat kernel (35K08) Harmonic analysis and PDEs (42B37)

Related Items

Dunkl translations, Dunkl-type BMO space, and Riesz transforms for the Dunkl transform on \(L^\infty \) ⋮ Weighted inequalities for multilinear fractional operators in Dunkl setting ⋮ Singular integrals in the rational Dunkl setting ⋮ Boundedness of bilinear Dunkl–Hausdorff operators on products of Lebesgue and Morrey spaces ⋮ Hardy spaces for the Dunkl harmonic oscillator ⋮ Dimension-free \(L^p\)-estimates for vectors of Riesz transforms in the rational Dunkl setting ⋮ Lipschitz and Triebel-Lizorkin spaces, commutators in Dunkl setting ⋮ Dimension‐free square function estimates for Dunkl operators ⋮ Sharp estimates for \(W\)-invariant Dunkl and heat kernels in the \(A_n\) case ⋮ Remarks on Dunkl translations of non-radial kernels ⋮ Sharp Li-Yau inequalities for Dunkl harmonic oscillators ⋮ 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 ⋮ Semigroup and Riesz transform for the Dunkl-Schrödinger operators ⋮ Existence of extremals of Dunkl-type Sobolev inequality and of Stein-Weiss inequality for Dunkl Riesz potential ⋮ Sharp estimates of radial Dunkl and heat kernels in the complex case \(A_n\) ⋮ Schrödinger operators with reverse Hölder class potentials in the Dunkl setting and their Hardy spaces ⋮ On semigroups generated by sums of even powers of Dunkl operators ⋮ On the representing measures of Dunkl's intertwining operator ⋮ Behavior of eigenvalues of certain Schrödinger operators in the rational Dunkl setting ⋮ Relative Nash-type and \(L^2\)-Sobolev inequalities in Dunkl setting ⋮ Hörmander's multiplier theorem for the Dunkl transform ⋮ Infinite dimensional systems of particles with interactions given by Dunkl operators ⋮ Local Riesz transform and local Hardy spaces on Riemannian manifolds with bounded geometry ⋮ Upper and lower bounds for the Dunkl heat kernel ⋮ Upper and lower bounds for Littlewood–Paley square functions in the Dunkl setting ⋮ The dual of the Hardy space associated with the Dunkl operators

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