Abstract
In this paper we introduce a conjugate class of Riesz transforms in the context of Laguerre polynomials. We prove their weak-type (1,1) and L p, 1<p<∞, boundedness with respect to the Laguerre measure. A similar result is known in the Hermite context, see Aimar et al. (Trans. Am. Math. Soc. 359(5), 2137–2154, 2007).
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Communicated by Fulvio Ricci.
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Forzani, L., Sasso, E. & Scotto, R. Weak-Type Inequality for Conjugate First Order Riesz-Laguerre Transforms. J Fourier Anal Appl 17, 854–878 (2011). https://doi.org/10.1007/s00041-010-9166-x
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DOI: https://doi.org/10.1007/s00041-010-9166-x