Héctor Cuenya

  • Citations Per Year
Learn More
The space L with this norm is a Banach space (see [1]). If E ∈ B and μ(E) > 0, then ∥ · ∥j,E is a seminorm on L(X). In the particular case, j (t) = t, we will use the notation ∥ · ∥p,E instead of ∥ · ∥j,E. Let N ⊂ M , N Î N, be the class of all algebraic polynomials of degree at most N, with real coefficients. Given E ∈ B , we recall that a polynomial gE Î(More)
Let ðO;A; P Þ be a measurable space and L A a sub-s-lattice of the s-algebra A: For X 2 L1ðO;A; P Þ we denote by PLX the set of conditional 1-mean (or best approximants) of X given L1ðLÞ (the set of all L-measurable and integrable functions). In this paper, we obtain characterizations of the elements in PLX ; similar to those obtained by Landers and Rogge(More)
Given f E L2(lR n), E > 0 and x E IR n we consider P(t) to be the polynomial of best approximation to f in the L2-norm by elements of IIm over the set x + EC, where C denote a suitable parallelepiped. Let T;'f(x) be the Qth-coefficient of P when it has been developed in the base {t"'/Q!}. In this paper we show that the operator T;' is a composition of a(More)
Let (Ω,A, μ) be a σ-finite nonatomic measure space and let Λw,φ be the Orlicz-Lorentz space. We study the Gateaux differentiability of the functional Ψw,φ(f) = ∞ ∫ 0 φ(f∗)w. More precisely we give an exact characterization of those points in the Orlicz-Lorentz space Λw,φ where the Gateaux derivative exists. This paper extends known results already on Lorent(More)
  • 1