36 citations · 234 across the 37 of their papers we have counts for
27 papers · 1 filter
Variation operators for semigroups associated with Fourier-Bessel expansions
Jorge J. Betancor, Alejandro J. Castro, Marta De León-Contreras
In this paper we establish -boundedness properties for variation operators defined by semigroups associated with Fourier-Bessel expansions.
Riesz transforms, Cauchy-Riemann systems and amalgam Hardy spaces
Al-Tarazi Assaubay, Jorge J. Betancor, Alejandro J. Castro +1
In this paper we study Hardy spaces , , modeled over amalgam spaces . We characterize $\mathcal{H}^{p,q}(…
BMO functions and Balayage of Carleson measures in the Bessel setting
Víctor Almeida, Jorge J. Betancor, Alejandro J. Castro +2
By we denote the space consisting of all those odd and bounded mean oscillation functions on R. In this paper we characterize the functions in with bounded su…
Variable exponent Hardy spaces associated with discrete Laplacians on graphs
Víctor Almeida, Jorge J. Betancor, Alejandro J. Castro +1
In this paper we develop the theory of variable exponent Hardy spaces associated with discrete Laplacians on infinite graphs. Our Hardy spaces are defined by square integrals, atom…
Oscillation of generalized differences of Hölder and Zygmund functions
Alejandro J. Castro, José G. Llorente, Artur Nicolau
In this paper we analyze the oscillation of functions having derivatives in the Hölder or Zygmund class in terms of generalized differences and prove that its growth is governed by…
Discrete harmonic analysis associated with ultraspherical expansions
Jorge J. Betancor, Alejandro J. Castro, Juan C. Fariña +1
We study discrete harmonic analysis associated with ultraspherical orthogonal functions. We establish weighted l^p-boundedness properties of maximal operators and Littlewood-Paley…
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…
On fundamental harmonic analysis operators in certain Dunkl and Bessel settings
Alejandro J. Castro, Tomasz Z. Szarek
We consider several harmonic analysis operators in the multi-dimensional context of the Dunkl Laplacian with the underlying group of reflections isomorphic to (als…
Riesz transforms and multipliers for the Bessel-Grushin operator
Víctor Almeida, Jorge J. Betancor, Alejandro J. Castro +1
We establish that the spectral multiplier associated to the differential operator $$ G_α=- Δ_x +\sum_{j=1}^m{{α_j^2-1/4}\over{x_j^2}}-|x|^2 Δ_y \; \text{on} (0,\inf…
UMD-valued square functions associated with Bessel operators in Hardy and BMO spaces
J. J. Betancor, A. J. Castro, L. Rodríguez-Mesa
We consider Banach valued Hardy and BMO spaces in the Bessel setting. Square functions associated with Poisson semigroups for Bessel operators are defined by using fractional deriv…
Square functions and spectral multipliers for Bessel operators in UMD spaces
Jorge J. Betancor, Alejandro J. Castro, Lourdes Rodriguez-Mesa
In this paper we consider square functions (also called Littlewood-Paley g-functions) associated to Hankel convolutions acting on functions in the Bochner-Lebesgue space $L^p((0,\i…
UMD Banach spaces and square functions associated with heat semigroups for Schrödinger and Laguerre operators
J. J. Betancor, A. J. Castro, J. C. Fariña +1
In this paper we define square functions (also called Littlewood-Paley-Stein functions) associated with heat semigroups for Schrödinger and Laguerre operators acting on functions w…
UMD Banach spaces and the maximal regularity for the square root of several operators
Víctor Almeida, Jorge J. Betancor, Alejandro J. Castro
In this paper we prove that the maximal -regularity property on the interval , , for Cauchy problems associated with the square root of Hermite, Bessel or Laguerre…
Square functions in the Hermite setting for functions with values in UMD spaces
Jorge J. Betancor, Alejandro J. Castro, Jezabel Curbelo +2
In this paper we characterize the Lebesgue Bochner spaces , , by using Littlewood-Paley -functions in the Hermite setting, provided that is…
-boundedness properties for the maximal operators for semigroups associated with Bessel and Laguerre operators
Jorge J. Betancor, Alejandro J. Castro, Pablo L. De Nápoli +2
In this paper we prove that the generalized (in the sense of Caffarelli and Calderón) maximal operators associated with heat semigroups for Bessel and Laguerre operators are weak t…
-radonifying operators and UMD-valued Littlewood-Paley-Stein functions in the Hermite setting on BMO and Hardy spaces
Jorge J. Betancor, Alejandro J. Castro, Jezabel Curbelo +2
In this paper we study Littlewood-Paley-Stein functions associated with the Poisson semigroup for the Hermite operator on functions with values in a UMD Banach space $\B.$ If we de…
Characterization of Banach valued BMO functions and UMD Banach spaces by using Bessel convolutions
Jorge J. Betancor, Alejandro J. Castro, Lourdes Rodríguez-Mesa
In this paper we consider the space of bounded mean oscillations and odd functions on taking values in a UMD Banach space . The functions in $…
Calderón-Zygmund operators in the Bessel setting for all possible type indices
Alejandro J. Castro, Tomasz Z. Szarek
In this paper we adapt the technique developed in [17] to show that many harmonic analysis operators in the Bessel setting, including maximal operators, Littlewood-Paley-Stein type…
Characterization of uniformly convex and smooth Banach spaces by using Carleson measures in Bessel settings
Jorge J. Betancor, Alejandro J. Castro, Lourdes Rodríguez-Mesa
In this paper we obtain new characterizations of the q-uniformly convex and smooth Banach spaces by using Carleson measures. These measures are defined by Poisson integral associat…
Characterization of UMD Banach spaces by imaginary powers of Hermite and Laguerre operators
Jorge J. Betancor, Alejandro J. Castro, Jezabel Curbelo +1
In this paper we characterize the Banach spaces with the UMD property by means of Lp-boundedness properties for the imaginary powers of the Hermite and Laguerre operators. In order…