Geodesic
$L^p $ boundedness of Riesz transforms for orthogonal polynomials in a general context
Liliana Forzani 1   ; Emanuela Sasso 2   ; Roberto Scotto 1
1 Departamento de Matemática Facultad de Ingeniería Química (UNL) Instituto de Matemática Aplicada del Litoral - IMAL (CONICET-UNL) 3000 Santa Fe, Argentina
2 Dipartimento di Matematica Università di Genova Genova, Italy
Studia Mathematica, Tome 231 (2015) no. 1, pp. 45-71 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Nowak and Stempak (2006) proposed a unified approach to the theory of Riesz transforms and conjugacy in the setting of multi-dimensional orthogonal expansions, and proved their boundedness on $L^2$. Following them, we give easy to check sufficient conditions for their boundedness on $L^p$, $1 \lt p \lt \infty $. We also discuss the symmetrized version of these transforms.
DOI : 10.4064/sm8221-1-2016
Keywords: nowak stempak proposed unified approach theory riesz transforms conjugacy setting multi dimensional orthogonal expansions proved their boundedness following easy check sufficient conditions their boundedness infty discuss symmetrized version these transforms

Liliana Forzani  1   ; Emanuela Sasso  2   ; Roberto Scotto  1

1 Departamento de Matemática Facultad de Ingeniería Química (UNL) Instituto de Matemática Aplicada del Litoral - IMAL (CONICET-UNL) 3000 Santa Fe, Argentina
2 Dipartimento di Matematica Università di Genova Genova, Italy 
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     title = {$L^p $ boundedness of {Riesz} transforms for orthogonal polynomials in a general context},
     journal = {Studia Mathematica},
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Liliana Forzani; Emanuela Sasso; Roberto Scotto. $L^p $ boundedness of Riesz transforms for orthogonal polynomials in a general context. Studia Mathematica, Tome 231 (2015) no. 1, pp. 45-71. doi: 10.4064/sm8221-1-2016

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