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The Lipschitz injective hull of Lipschitz operator ideals and applications
(Banach Mathematical Research Group, 2020-03)
We introduce and study the Lipschitz injective hull of Lipschitz operator ideals defined between metric spaces. We show some properties and apply the results to the ideal of Lipschitz p-nuclear operators, obtaining the ...
Espacios Lipschitz generalizados y operadores invariantes por traslaciones
(1997-02-27)
We extend to context of the Generalized Lipschitz spaces and to context of the Orlicz spaces, the result of Stein and Zygmund about the Lp boundedness of translation invariant operators between Lipschitz spaces. They ...
Extrapolation and weighted norm inequalities between Lebesgue and Lipschitz spaces in the variable exponent context
(Elsevier, 2016-04)
We give extrapolation results starting from weighted inequalities between Lebesgue and Lipschitz spaces, given by sup B kwχBk∞ |B| 1+ δ n ˆ B |f(x) − mB(f)| dx ≤ C kgwks , (0.1) where 1 < β < ∞, 0 ≤ δ < 1, δ n = 1 β − 1 s ...
Compensated convexity methods for approximations and interpolations of sampled functions in euclidean spaces: Theoretical foundations
(Society for Industrial and Applied Mathematics, 2016-12)
We introduce Lipschitz continuous and C1;1 geometric approximation and interpolation methods for sampled bounded uniformly continuous functions over compact sets and over complements of bounded open sets in Rn by using ...
Lipschitz type smoothness of the fractional integral on variable exponent spaces
(Elsevier, 2013-02)
We give conditions on p(·) in order to assure boundedness of the fractional integral operator I_alpha from strong and weak L^p(·) spaces into suitable integral Lipschitz--type spaces.
On Besov regularity of temperatures
(Birkhauser Boston Inc, 2010-12)
We prove space-time parabolic Besov regularity in terms of integrability of Besov norms in the space variable for solutions of the heat equation on cylindrical regions based on Lipschitz domains.
Endpoint Estimates of Commutators of Singular Integrals vs. Conditions on the Symbol
(Birkhauser Boston Inc, 2020-01)
Endpoint estimates of commutators Tb of singular integrals T, are studied over general spaces that include, in particular, BMO and Lipschitz spaces. We also characterize the conditions of the symbol b in order to obtain ...
The Riesz potential as a multilinear operator into general BMOβ spaces
(Springer Science, 2011-03)
Given α > 0 and a space of homogeneous type X, n-normal, with n ℝ+, we consider an extension of the standard multilinear fractional integral on Lp1 × ... × Lpk for the range of 1/pi = 1/p1...+1/pk -α/n ≤ 0. We show that ...
Applications of the integration of essentially bounded functions and classification of asymmetric spacesAplicaciones de la integración de funciones esencialmente acotadas y clasificación de espacios asimétricos
(2021)
This work corresponds to a Doctorate Thesis dissertation for obtaining the PhD Degree in Engineering Science (Mention: Mathematical Modelling). The dissertation is inscribed in the broad area of Variational and Functional ...