36 citations · 234 across the 37 of their papers we have counts for
5 papers · 2 filters
Variable exponent Sobolev spaces associated with Jacobi expansions
V. Almeida, J. J. Betancor, A. J. Castro +2
In this paper we define variable exponent Sobolev spaces associated with Jacobi expansions. We prove that our generalized Sobolev spaces can be characterized as variable exponent p…
Solutions of Weinstein equations representable by Bessel Poisson integrals of BMO functions
Jorge J. Betancor, Alejandro J. Castro, Juan C. Fariña +1
We consider the Weinstein type equation on , where , with . In…
Bounds for partial derivatives: necessity of UMD and sharp constants
Alejandro J. Castro, Tuomas P. Hytönen
We prove the necessity of the UMD condition, with a quantitative estimate of the UMD constant, for any inequality in a family of bounds between different partial derivatives…
Riesz-Jacobi transforms as principal value integrals
Alejandro J. Castro, Adam Nowak, Tomasz Z. Szarek
We establish an integral representation for the Riesz transforms naturally associated with classical Jacobi expansions. We prove that the Riesz-Jacobi transforms of odd orders expr…
Conical square functions associated with Bessel, Laguerre and Schrödinger operators in UMD Banach spaces
Jorge J. Betancor, Alejandro J. Castro, Juan C. Fariña +1
In this paper we consider conical square functions in the Bessel, Laguerre and Schrödinger settings where the functions take values in UMD Banach spaces. Following a recent paper o…