Multiparameter ergodic Cesàro-α averages

Let (X,F,ν) be a σ-finite measure space. Associated with k Lamperti operators on Lp(ν), T1,…,Tk, nˉ=(n1,…,nk)∈Nk and αˉ=(α1,…,αk) with 0<αj≤1, we define the ergodic Cesàro-αˉ averages Rnˉ,αˉf=1∏kj=1Aαjnj∑ik=0nk⋯∑i1=0n1∏j=1kAαj−1nj−ijTikk⋯Ti11f. For these averages we prove the almost everywhere convergence on X and the convergence in the Lp(ν) norm, when n1,…,nk→∞ independently, for all f∈Lp(dν) with p>1/α∗ where α∗=min1≤j≤kαj. In the limit case p=1/α∗, we prove that the averages Rnˉ,αˉf converge almost everywhere on X for all f in the Orlicz–Lorentz space Λ(1/α∗,φm−1) with φm(t)=t(1+log+t)m. To obtain the result in the limit case we need to study inequalities for the composition of operators Ti that are of restricted weak type (pi,pi). As another application of these inequalities we also study the strong Cesàro-αˉ continuity of functions.Fil: Bernardis, Ana Lucia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Crescimbeni, Raquel Liliana. Universidad Nacional del Comahue; ArgentinaFil: Ferrari Freire, Cecilia. Universidad Nacional del Comahue; Argentin

A note on wavelet expansions for dyadic BMO functions in spaces of homogeneous type

We give a characterization of dyadic BMO spaces in terms of Haarwavelet coefficients in spaces of homogeneous type.Fil: Crescimbeni, Raquel Liliana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Confluencia. Instituto de Investigación En Tecnologías y Ciencias de la Ingeniería. Universidad Nacional del Comahue. Instituto de Investigación En Tecnologías y Ciencias de la Ingeniería; Argentina. Universidad Nacional del Comahue. Facultad de Economía y Administración. Departamento de Matemática; ArgentinaFil: Nowak, Luis Maria Ricardo. Universidad Nacional del Comahue. Facultad de Economía y Administración. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Confluencia. Instituto de Investigación En Tecnologías y Ciencias de la Ingeniería. Universidad Nacional del Comahue. Instituto de Investigación En Tecnologías y Ciencias de la Ingeniería; Argentin

Two-weighted inequalities for the fractional integral associated to the Schrödinger operator

In this article we prove that the fractional integral operator associated to the Schrödinger second order differential operator L-α/2=(-Δ + V)-α/2maps with continuity weak Lebesgue space Lp,∞(v) into weighted Campanato-Hölder type spaces BMOβL(w), thus improving regularity under appropriate conditions on the pair of weights (v,w) and the parameters p, α and β. We also prove the continuous mapping from BMOβL(v) to BMOγL(w) for adequate pair of weights. Our results improve those known for the same weight in both sides of the inequality and they also enlarge the families of weights known for the classical fractional integral associated to the Laplacian operator L = -Δ.Fil: Crescimbeni, Raquel Liliana. Universidad Nacional del Comahue; ArgentinaFil: Hartzstein, Silvia Inés. Universidad Nacional del Litoral; ArgentinaFil: Salinas, Oscar Mario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentin

A new proof of Harnack's inequality for elliptic partial differential equations in divergence form

In this paper we give a new proof of Harnack's inequality for elliptic operator in divergence form. We imitate the proof given by Caffarelli for operators in nondivergence form

Multilinear Cesàro maximal operators

The study of the almost everywhere convergence of the product of m Cesàro-α averages leads to the characterization of the boundedness of the associated multi(sub)linear maximal operator. We characterize weighted weak type and strong type inequalities for this operator, extending results by Lerner et al. [A. Lerner, S. Ombrosi, C. Pérez, R. Torres, R. Trujillo-González, New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory, Adv. Math. 220 (2009) 1222?1264.]. We also study the restricted weak type inequalities which are of particular interest in our case (they were not considered by Lerner et al.).Fil: Bernardis, Ana Lucia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Crescimbeni, Raquel Liliana. Universidad Nacional del Comahue; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Martín Reyes, Francisco Javier. Universidad de Málaga; Españ

The rho-variation as an operator between maximal operators and singular integrals

The ρ-variation and the oscillation of the heat and Poisson semigroups of the Laplacian and Hermite operators (i.e. Δ and −Δ + |x|2) are proved to be bounded from Lp(Rn w(x)dx) into itself (fromL1(Rn w(x)dx) into weak-L1(Rn w(x)dx) in the case p = 1) for 1 ≤ p < ∞ and w being a weight in the Muckenhoupt?s Ap class. In the case p = ∞ it is proved that these operators do not map L∞ into itself. Even more, they map L∞ into BMO but the range of the image is strictly smaller that the range of a general singular integral operator.Fil: Crescimbeni, Raquel Liliana. Universidad Nacional del Comahue. Facultad de Economía y Administración. Departamento de Matemática; ArgentinaFil: Macias, Roberto Aristobulo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Menarguez, Teresa. Universidad Autónoma de Madrid. Facultad de Ciencias; EspañaFil: Torrea, Jose Luis. Universidad Autónoma de Madrid. Facultad de Ciencias; EspañaFil: Viviani, Beatriz Eleonora. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentin