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$L^{p}$ bounds for spectral multipliers on rank one NA-groups with roots not all positive

Emilie David-Guillou (2004)

Colloquium Mathematicae

We consider a family of non-unimodular rank one NA-groups with roots not all positive, and we show that on these groups there exists a distinguished left invariant sub-Laplacian which admits a differentiable $L^{p}$ functional calculus for every p ≥ 1.

$L^{p}$ -improving properties of measures supported on curves on the Heisenberg group. II

Silvia Secco (2002)

Bollettino dell'Unione Matematica Italiana

$L^{p}$ - $L^{q}$ estimates are obtained for convolution operators by finite measures supported on curves in the Heisenberg group whose tangent vector at the origin is parallel to the centre of the group.

$L^{p} - L^{q}$ -estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. II.

Cowling, Michael, Giulini, Saverio, Meda, Stefano (1995)

Journal of Lie Theory

$L^{p} - L^{q}$ estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. III

Michael Cowling, Saverio Giulini, Stefano Meda (2001)

Annales de l’institut Fourier

Let $X$ be a symmetric space of the noncompact type, with Laplace–Beltrami operator $- ℒ$ , and let $[b, \infty)$ be the $L^{2} (X)$ -spectrum of $ℒ$ . For $τ$ in $ℂ$ such that $Re τ \geq 0$ , let $𝒫_{τ}$ be the operator on $L^{2} (X)$ defined formally as $\exp (- τ {(ℒ - b)}^{1 / 2})$ . In this paper, we obtain $L^{p} - L^{q}$ operator norm estimates for $𝒫_{τ}$ for all $τ$ , and show that these are optimal when $τ$ is small and when $| \arg τ |$ is bounded below $π / 2$ .

$L^{p}$ -Multiplier transference induced by representations in Hilbert space

Earl Berkson, T. Gillespie, Paul Muhly (1989)

Studia Mathematica

$L^{p}$ -multipliers for the Laguerre expansions

Jolanta Dlugosz (1987)

Colloquium Mathematicae

Le théorème des idempotents dans $B (G)$

B. Host (1986)

Bulletin de la Société Mathématique de France

Lipschitz classes and Poisson integrals on stratified groups

G. Folland (1979)

Studia Mathematica

Lipschitz Spaces on Compact Lie Groups.

Stefano Meda, Rita Pini (1988)

Monatshefte für Mathematik

Littlewood-Paley theory on solenoids

Nakhlé Asmar, Stephen Montgomery-Smith (1993)

Colloquium Mathematicae

Local Hardy spaces on Chébli-Trimèche hypergroups

Walter Bloom, Zengfu Xu (1999)

Studia Mathematica

We investigate the local Hardy spaces $h^{p}$ on Chébli-Trimèche hypergroups, and establish the equivalence of various characterizations of these in terms of maximal functions and atomic decomposition.

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