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Musielak-Orlicz-bumps and Bloom type estimates for commutators of Calderón-Zygmund and fractional integral operators on generalized Zygmund spaces via sparse operators
(Akadémiai Kiadó, 2021-04-10)
We study continuity properties for commutators of Calderón-Zygmund and fractional integral operators between generalized Zygmund spaces of L log L type, in the variable exponent setting with different weights. In order to ...
A1 bounds for Calderón-Zygmund operators related to a problem of Muckenhoupt and Wheeden
(International Press Boston, 2009-12)
We obtain an Lp(ω) bound for Calderón-Zygmund operators T when w∈ A1. This bound is sharp both with respect to ||ω||A1 and with respect to p. As a result, we get a new L1,∞°(ω) estimate for T related to a problem of ...
On the Calderón-Zygmund structure of Petermichl's kernelSur la structure Calderón-Zygmund du noyau de Petermichl
(Elsevier France-editions Scientifiques Medicales Elsevier, 2018-05)
We show that Petermichl's dyadic operator P (Petermichl (2000) [8]) is a Calderón–Zygmund-type operator on an adequate metric normal space of homogeneous type. We also compare the maximal operators associated with truncations ...
New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory
(Academic Press Inc Elsevier Science, 2009-03-01)
A multi(sub)linear maximal operator that acts on the product of m Lebesgue spaces and is smaller than the m-fold product of the Hardy-Littlewood maximal function is studied. The operator is used to obtain a precise control ...
On the composition of the integral and derivative operators of functional order
(Universitatis Carolinae, 2003-03)
In this work we show that the composition of the integral and derivative operators of order phi, T_phi = D_phi◦I_phi, is a singular integral operator.This result in addition with the results obtained in [HV2] of boundedness ...
Extrapolation for multilinear Muckenhoupt classes and applications
(Elsevier Science, 2020-10-28)
In this paper we solve a long standing problem about the multivariable Rubio de Francia extrapolation theorem for the multilinear Muckenhoupt classes , which were extensively studied by Lerner et al. and which are the ...
Optimal exponents in weighted estimates without examples
(International Press Boston, 2015-04-13)
We present a general approach for proving the optimality of the exponents on weighted estimates. We show that if an operator T satisfies a bound like ∥ T ∥ Lp(w) ≤ c [w]βAp w ε Ap, then the optimal lower bound for β is ...
Weighted inequalities for fractional type operators with some homogeneous kernels
(Springer Heidelberg, 2013-03)
In this paper, we study integral operators of the form, where Ai are certain invertible matrices, αi > 0, 1 ≤ i ≤ m, α1 + ... + αm = n - α, 0 ≤ α < n. For, we obtain the Lp(ℝn, wp) - Lq(ℝn,wq) boundedness for weights w in ...
Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden
(Birkhäuser Publishing, 2009)
Hörmander conditions for vector-valued kernels of singular integrals and their commutators
(Unión Matemática Argentina, 2019-06)
We study Coifman type estimates and weighted norm inequalities for singular integral operators and their commutators, given by the convolution with a vector-valued kernel. We define a weaker Hörmander type condition ...