Emanuela Sasso
Abstract
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We prove that the first order Riesz transforms associated to the Laguerre semigroup are weak-type (1, 1). We also present a counterexample showing that for the Riesz transforms of order three or higher the weak type (1, 1) estimate fails.
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We prove that the first order Riesz transforms associated to the Laguerre semigroup are weak-type (1, 1). We also present a counterexample showing that for the Riesz transforms of order three or higher the weak type (1, 1) estimate fails.
Key concepts: Mathematics, Laguerre polynomials, Riesz transform, Counterexample, M. Riesz extension theorem, Type (biology), Riesz potential, Order (exchange)