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In 1951 V. Jarnik constructed two continuous functions whose Volterra convolution is nowhere differentiable. We generalize Jarnik's results by proving that the set of such functions is maximal lineable. This would shed some light on a question p[...]texto impreso
Araujo, G. ; Jiménez Rodríguez, P. ; Muñoz-Fernández, Gustavo A. ; Seoane-Sepúlveda, Juan B. | Elsevier | 2017In this paper, equivalence constants between various polynomial norms are calculated. As an application, we also obtain sharp values of the Hardy Littlewood constants for 2-homogeneous polynomials on l(p)(2) spaces, 2texto impreso
Jiménez Rodríguez, P. ; Maghsoudi, S. ; Muñoz-Fernández, Gustavo A. ; Seoane-Sepúlveda, Juan B. | Belgian Mathematical Soc Triomphe | 2016It is known that there is not a two dimensional linear space in R-R every non-zero element of which is an injective function. Here, we generalize this result to arbitrarily large dimensions. We also study the convolution of non differentiable fu[...]texto impreso
Araujo, G. ; Jiménez Rodríguez, P. ; Muñoz-Fernández, Gustavo A. ; Núñez Alarcón, D. ; Pellegrino, D. ; Seoane-Sepúlveda, Juan B. ; Serrano Rodríguez, D.M. | Springer | 2015-03We investigate the behavior of the constants of the polynomial Hardy-Littlewood inequality.texto impreso
Araujo, G. ; Jiménez Rodríguez, P. ; Muñoz-Fernández, Gustavo A. ; Nuñez-Alarcon, D. ; Pellagrino, D. ; Seoane-Sepúlveda, Juan B. ; Serrano-Rodriguez, D.M. | Birkhäuser Verlag | 2015We investigate the behavior of the constants of the polynomial Hardy-Littlewood inequality.texto impreso
Campos, J.R. ; Jiménez Rodríguez, P. ; Muñoz-Fernández, Gustavo A. ; Pellegrino, D. ; Seoane-Sepúlveda, Juan B. | Elsevier | 2015Abstract. It was recently proved by Bayart et al. that the complex polynomial Bohnenblust–Hille inequality is subexponential. We show that, for real scalars, this does no longer hold. Moreover, we show that, if DR,m stands for the real Bohnenblu[...]texto impreso
Araujo, G. ; Jiménez Rodríguez, P. ; Muñoz-Fernández, Gustavo A. ; Seoane-Sepúlveda, Juan B. | Heldermann Verlag | 2017A number of sharp inequalities are proved for the space P (2D (?/4)) of 2-homogeneous polynomials on ?2 endowed with the supremum norm on the sector D (?/4) := {ei? : ? ? [0, ?/4]}. Among the main results we can find sharp Bernstein and Markov i[...]texto impreso
Jiménez Rodríguez, P. ; Muñoz-Fernández, Gustavo A. ; Murillo Arcila, M. ; Seoane-Sepúlveda, Juan B. | Taylor & Francis | 2015In this paper we prove that the complex polynomial Bohnenblust-Hille constant for 2-homogeneous polynomials in C2 is exactly 4q 3 2 . We also give the exact value of the real polynomial Bohnenblust-Hille constant for 2-homogeneous polynomials in[...]texto impreso
Conejero, Jose A. ; Jiménez Rodríguez, P. ; Muñoz-Fernández, Gustavo A. ; Seoane-Sepúlveda, Juan B. | Mathematical Association of America | 2014-01The Identity Theorem states that an analytic function (real or complex) on a connected domain is uniquely determined by its values on a sequence of distinct points that converge to a point of its domain. This result is not true in general in the[...]
