New York Journal of Mathematics
Volume 23 (2017) 1327-1356


Giancarlo Mauceri, Stefano Meda, and Maria Vallarino

Endpoint results for spherical multipliers on noncompact symmetric spaces

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Published: October 6, 2017
Keywords: Hardy spaces, atoms, noncompact symmetric spaces, spherical multipliers
Subject: 30H10, 42B15, 42B20, 53C35

In this paper we prove boundedness results on atomic Hardy type spaces for multipliers of the spherical transform on noncompact symmetric spaces of arbitrary rank. The multipliers we consider satisfy either inhomogeneous or homogeneous Mihlin-Hörmander type conditions. In particular, we are able to treat the case of {strongly singular multipliers} whose convolution kernels are not integrable at infinity. Thus our results apply also to negative and imaginary powers of the Laplacian.


Work partially supported by PRIN 2015 "Real and complex manifolds: geometry, topology and harmonic analysis". The authors are members of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM)

Author information

Giancarlo Mauceri:
Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, 16146 Genova, Italy

Stefano Meda:
Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, via R. Cozzi 53, I-20125 Milano, Italy

Maria Vallarino:
Dipartimento di Scienze Matematiche "Giuseppe L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy