Triebel-Lizorkin spaces associated with Laguerre and Hermite expansions

DOI10.1090/S0002-9939-97-03950-6zbMath0915.42018OpenAlexW1521274738MaRDI QIDQ4372408

Jacek Dziubański

Publication date: 11 December 1997

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-97-03950-6

zbMATH Keywords

Triebel-Lizorkin spacesHeisenberg groupsymbolic calculusLaguerre expansionsHermite expansions

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) General harmonic expansions, frames (42C15) General properties and structure of complex Lie groups (22E10)

Related Items

Sub-exponentially localized kernels and frames induced by orthogonal expansions ⋮ Weighted embeddings for function spaces associated with Hermite expansions ⋮ Besov spaces for the Schrödinger operator with barrier potential ⋮ Local Approximation Using Hermite Functions ⋮ Decomposition of spaces of distributions induced by Hermite expansions ⋮ A continuous characterization of Triebel-Lizorkin spaces associated with Hermite expansions ⋮ Approximation and localized polynomial frame on conic domains ⋮ Besov and {T}riebel-{L}izorkin spaces associated with {L}aguerre expansions of {H}ermite type ⋮ On the wave equation associated to the Hermite and the twisted Laplacian ⋮ Littlewood-Paley theorem for Schrödinger operators ⋮ Littlewood-Paley theorem for Schrödinger operators ⋮ A Fourier-invariant method for locating point-masses and computing their attributes ⋮ Decomposition of Triebel-Lizorkin and Besov spaces in the context of Laguerre expansions ⋮ Pseudo-multipliers and smooth molecules on Hermite Besov and Hermite Triebel-Lizorkin spaces ⋮ On Jacobi polynomials \(\mathscr{P}_k^{(\alpha,\beta)}\) and coefficients \(c_j^{\ell}(\alpha,\beta)\) \((k\geq 0, \ell =5,6; 1\leq j\leq \ell; \alpha,\beta > -1)\) ⋮ Paley-Littlewood decomposition for sectorial operators and interpolation spaces ⋮ Interpolation theorems for self-adjoint operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On spaces of Triebel-Lizorkin type
• Almost Everywhere Summability on Nilmanifolds
• Almost everywhere convergence of some summabillity methods for Laguerre series
• A functional calculus for Rockland operators on nilpotent Lie groups
• Hermite and Laguerre wave packet expansions
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• Triebel-Lizorkin spaces for Hermite expansions
• Some Maximal Inequalities