Recent Developments in Real and Harmonic Analysis: In Honor of Carlos Segovia

Featuring a collection of invited chapters dedicated to Carlos Segovia, this volume examines the developments in real and harmonic analysis. It includes topics such as: Vector-valued singular integral equations; Harmonic analysis related to Hermite expansions; Gas flow in porous media; and, Global well-posedness of the KPI Equatio

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