Generalized Lorentz spaces and applications

DOI10.1155/2013/302941zbMath1296.46026OpenAlexW2154698197WikidataQ59013935 ScholiaQ59013935MaRDI QIDQ2443698

Hatem Mejjaoli

Publication date: 8 April 2014

Published in: Journal of Function Spaces and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/302941

zbMATH Keywords

Lorentz spacesStrichartz estimatesDunkl-Besov spaces

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items (7)

Rellich, Gagliardo-Nirenberg, Trudinger and Caffarelli-Kohn-Nirenberg inequalities for Dunkl operators and applications ⋮ Restriction theorem for the Fourier-Dunkl transform. I: Cone surface ⋮ Restriction theorem for the Fourier-Dunkl transform and its applications to Strichartz inequalities ⋮ Existence of extremals of Dunkl-type Sobolev inequality and of Stein-Weiss inequality for Dunkl Riesz potential ⋮ Sobolev-type inequalities for Dunkl operators ⋮ Hardy-type inequalities for Dunkl operators with applications to many-particle Hardy inequalities ⋮ Upper and lower bounds for Littlewood–Paley square functions in the Dunkl setting

Cites Work

• Fractional Gagliardo-Nirenberg and Hardy inequalities under Lorentz norms
• Riesz transform and Riesz potentials for Dunkl transform
• Strichartz estimates for the Dunkl wave equation and application
• Generalized Hermite polynomials and the heat equation for Dunkl operators
• The Dunkl transform
• Generalized Besov spaces and their applications
• Nonsymmetric Jack polynomials and integral kernels
• A uniform proof of the Macdonald-Mehta-Opdam identity for finite Coxeter groups
• Real interpolation method, Lorentz spaces and refined Sobolev inequalities
• Convolution operator and maximal function for the Dunkl transform
• Global well-posedness and scattering for a class of nonlinear Dunkl-Schrödinger equations
• Dunkl heat semigroup and applications
• Differential-Difference Operators Associated to Reflection Groups
• Integral Kernels with Reflection Group Invariance
• Endpoint Strichartz estimates
• Dunkl Operator Formalism for Quantum Many-Body Problems Associated with Classical Root Systems
• Paley-Wiener Theorems for the Dunkl Transform and Dunkl Translation Operators
• A positive radial product formula for the Dunkl kernel
• Lorentz space extension of Strichartz estimates
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