Artículo
Hausdorff-Young-type inequalities for vector-valued Dirichlet series
Fecha de publicación:
08/2020
Editorial:
American Mathematical Society
Revista:
Transactions Of The American Mathematical Society
ISSN:
0002-9947
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We study Hausdorff-Young-type inequalities for vector-valued Dirichlet series which allow us to compare the norm of a Dirichlet series in the Hardy space Hp(X) with the q-norm of its coefficients. In order to obtain inequalities completely analogous to the scalar case, a Banach space must satisfy the restrictive notion of Fourier type/cotype. We show that variants of these inequalities hold for the much broader range of spaces enjoying type/cotype. We also consider Hausdorff-Young-type inequalities for functions defined on the infinite torus T ∞ or the boolean cube {-1, 1}∞. As a fundamental tool we show that type and cotype are equivalent to a hypercontractive homogeneous polynomial type and cotype, a result of independent interest.
Palabras clave:
HAUSDORFF-YOUNG INEQUALITIES
,
DIRICHLET SERIES
,
BANACH SPACES
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Articulos(IMAS)
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Citación
Carando, Daniel Germán; Marceca, Felipe; Sevilla Peris, Pablo; Hausdorff-Young-type inequalities for vector-valued Dirichlet series; American Mathematical Society; Transactions Of The American Mathematical Society; 373; 8; 8-2020; 5627-5652
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