Let S be a Damek-Ricci space, and Δ be a distinguished Laplacean on S which is left invariant and selfadjoint in L<sup>2</sup>(ρ). We prove that S is a Calderón-Zygmund space with respect to the right Haar measure ρ and the left invariant distance. We give sufficient conditions of Hörmander type on a multiplier m so that the operator m(Δ) is bounded on L<sup>p</sup>(ρ) when 1 < p < ∞, and of weak type (1, 1). © 2007 Heldermann Verlag
Vallarino, M. (2007). Spectral multipliers on Damek--Ricci spaces. JOURNAL OF LIE THEORY, 17(1), 163-189.
Spectral multipliers on Damek--Ricci spaces
Vallarino, M
2007
Abstract
Let S be a Damek-Ricci space, and Δ be a distinguished Laplacean on S which is left invariant and selfadjoint in L2(ρ). We prove that S is a Calderón-Zygmund space with respect to the right Haar measure ρ and the left invariant distance. We give sufficient conditions of Hörmander type on a multiplier m so that the operator m(Δ) is bounded on Lp(ρ) when 1 < p < ∞, and of weak type (1, 1). © 2007 Heldermann Verlag
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