# Riesz transforms and multipliers for the Grushin operator

Source: [Riesz transforms and multipliers for the Grushin operator](<https://www.sota2.com/research/paper/68fa4f671e209131ce96311e>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T10:17:43.678Z

Authors: K.Jotsaroop, P.K.Sanjay, S. Thangavelu

Published: 2011-10-14T14:50:14.000Z

## Abstract

We show that Riesz transforms associated to the Grushin operator G = -\\Delta - \|x\|^2\\partial\_t^2 are bounded on L^p(R^n+1). We also establish an analogue of H\\"ormander-Mihlin multiplier theorem and study Bochner-Riesz means associated to the Grushin operator. The main tools used are Littlewood-Paley theory and an operator valued Fourier multiplier theorem due to L. Weis.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1110.3227>)

[PDF](<https://arxiv.org/pdf/1110.3227.pdf>)