Vector-valued Calderón-Zygmund theory applied to tent spaces
Vector-valued Calderón-Zygmund theory and Carleson measures on spaces of homogeneous nature
The work of José Luis Rubio de Francia (I).
The aim of these pages is to give the reader an idea about the first part of the mathematical life of José Luis Rubio de Francia.
Parabolic differential equations and vector-valued Fourier analysis
Weighted inequalities for commutators of fractional and singular integrals.
Some Banach techniques in vector-valued Fourier analysis
Pluriharmonic functions on symmetric tube domains with BMO boundary values
Let 𝓓 be a symmetric Siegel domain of tube type and S be a solvable Lie group acting simply transitively on 𝓓. Assume that L is a real S-invariant second order operator that satisfies Hörmander's condition and annihilates holomorphic functions. Let H be the Laplace-Beltrami operator for the product of upper half planes imbedded in 𝓓. We prove that if F is an L-Poisson integral of a BMO function and HF = 0 then F is pluriharmonic. Some other related results are also considered.
The two weight problem for operators in the upper half-plane
Vector-valued inequalities with weights.
This paper deals with the following problem: Let T be a given operator. Find conditions on v(x) (resp. u(x)) such that ∫ |Tf(x)|pu(x) dx ≤ C ∫ |f(x)|pv(x) dx is satisfied for some u(x) (resp. v(x)). Using vector-valued inequalities the problem is solved for: Carleson's maximal operator of Fourier partial sums, Littlewood-Paley square functions, Hilbert transform of functions valued in...
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