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Weighted Lorentz spaces: Sharp mixed A<inf>p</inf> − A<inf>∞</inf> estimate for maximal functions
(2023-03-15)
We prove the sharp mixed Ap−A∞ weighted estimate for the Hardy-Littlewood maximal function in the context of weighted Lorentz spaces, namely [Formula presented] where [Formula presented]. Our method is rearrangement free ...
Sawyer-type inequalities for Lorentz spaces
(2022-06)
The Hardy-Littlewood maximal operator M satisfies the classical Sawyer-type estimate ∥Mfv∥L1,∞(uv)≤Cu,v‖f‖L1(u),where u∈ A1 and uv∈ A∞. We prove a novel extension of this result to the general restricted weak type case. ...
Degenerate Poincare-Sobolev inequalities
(2021)
Abstract. We study weighted Poincar ́e and Poincar ́e-Sobolev type in- equalities with an explicit analysis on the dependence on the Ap con- stants of the involved weights. We obtain inequalities of the form with different ...
Extensions of the John-Nirenberg theorem and applications
(2021)
The John–Nirenberg theorem states that functions of bounded mean oscillation are
exponentially integrable. In this article we give two extensions of this theorem. The first one
relates the dyadic maximal function to the ...
Self-improving Poincaré-Sobolev type functionals in product spaces
(2021)
In this paper we give a geometric condition which ensures
that (q, p)-Poincar´e-Sobolev inequalities are implied from generalized
(1, 1)-Poincar´e inequalities related to L
1
norms in the context of product
spaces. ...
A note on generalized Fujii-Wilson conditions and BMO spaces
(2020-07-01)
In this note we generalize the definition of the Fujii-Wilson condition providing quantitative characterizations of some interesting classes of weights, such as A∞, A∞weak and Cp, in terms of BMO type spaces suited to them. ...
$A_1$ theory of weights for rough homogeneous singular integrals and commutators
(2019)
Quantitative $A_1-A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $\BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved:
\[
\|T_\Omega ...
Regularity of maximal functions on Hardy–Sobolev spaces
(2018-12-01)
We prove that maximal operators of convolution type associated to smooth kernels are bounded in the homogeneous Hardy–Sobolev spaces H1,p(Rd) when p > d/(d + 1). This range of exponents is sharp. As a by-product of the ...
Vector-valued operators, optimal weighted estimates and the $C_p$ condition
(2018-09)
In this paper some new results concerning the $C_p$ classes introduced by Muckenhoupt and later extended by Sawyer, are provided. In particular we extend the result to the full range expected $p>0$, to the weak norm, to ...
Proof of an extension of E. Sawyer's conjecture about weighted mixed weak-type estimates
(2018-09)
We show that if $v\in A_\infty$ and $u\in A_1$, then there is a constant $c$ depending on the $A_1$ constant of $u$ and the $A_{\infty}$ constant of $v$ such that
$$\Big\|\frac{ T(fv)} {v}\Big\|_{L^{1,\infty}(uv)}\le c\, ...