T
+34 946 567 842
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+34 946 567 843
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aperez@bcamath.org
Information of interest
- Orcid: 0000-0002-8128-1099
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$A_1$ theory of weights for rough homogeneous singular integrals and commutators
Pérez, C.
; Rivera-Ríos, I.P.; Roncal, L. (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 ...
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$A_1$ theory of weights for rough homogeneous singular integrals and commutators
Pérez, C.; Rivera-Ríos, I.P.; Roncal, L. (2016-07-01)
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 ...
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Borderline Weighted Estimates for Commutators of Singular Integrals
Pérez, C.; Rivera-Ríos, I.P. (2016-07-01)
In this paper we establish the following estimate \[ w\left(\left\{ x\in\mathbb{R}^{n}\,:\,\left|[b,T]f(x)\right| > \lambda\right\} \right)\leq \frac{c_{T}}{\varepsilon^{2}}\int_{\mathbb{R}^{n}}\Phi\left(\|b\|_{BMO}\f ...
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Degenerate Poincare-Sobolev inequalities
Pérez, C.; Rela, E. (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 ...
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Extensions of the John-Nirenberg theorem and applications
Canto, J.; Pérez, C. (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 ...
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Mixed weak type estimates: Examples and counterexamples related to a problem of E. Sawyer
Ombrosi, S.; Pérez, C. (2016-01-01)
In this paper we study mixed weighted weak-type inequal- ities for families of functions, which can be applied to study classic operators in harmonic analysis. Our main theorem extends the key result from [CMP2].
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A note on generalized Fujii-Wilson conditions and BMO spaces
Ombrosi, S.; Pérez, C.; Rela, E.; Rivera-Ríos, I. (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. ...
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A note on the off-diagonal Muckenhoupt-Wheeden conjecture
Cruz-Uribe, D.; Martell, J.M.; Pérez, C. (2016-07-01)
We obtain the off-diagonal Muckenhoupt-Wheeden conjecture for Calderón-Zygmund operators. Namely, given $1 < p < q < \infty$ and a pair of weights $(u; v)$, if the Hardy-Littlewood maximal function satisfies the following ...
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Proof of an extension of E. Sawyer's conjecture about weighted mixed weak-type estimates
Li, K.; Ombrosi, S.; Pérez, C. (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\, ...
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Quantitative weighted mixed weak-type inequalities for classical operators
Ombrosi, S.; Pérez, C.; Recchi, J. (2016-06-30)
We improve on several mixed weak type inequalities both for the Hardy-Littlewood maximal function and for Calderón-Zygmund operators. These type of inequalities were considered by Muckenhoupt and Wheeden and later on by ...
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Regularity of maximal functions on Hardy–Sobolev spaces
Pérez, C.; Picón, T.; Saari, Olli; Sousa, Mateus (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 ...
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Reverse Hölder Property for Strong Weights and General Measures
Luque, T.; Pérez, C.; Rela, E. (2016-06-30)
We present dimension-free reverse Hölder inequalities for strong $A^{\ast}_p$ weights, $1 \le p < \infty$. We also provide a proof for the full range of local integrability of $A^{\ast}_1$ weights. The common ingredient ...
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Three Observations on Commutators of Singular Integral Operators with BMO Functions
Pérez, C.; Rivera-Ríos, I.P. (2016-07-01)
Three observations on commutators of Singular Integral Operators with BMO functions are exposed, namely 1 - The already known subgaussian local decay for the commutator, namely $\[\frac{1}{|Q|}\left|\left\{x\in Q\, : ...
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Vector-valued operators, optimal weighted estimates and the $C_p$ condition
Cejas, M.E.; Li, K.; Pérez, C.; Rivera-Ríos, I.P. (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 ...
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Weighted norm inequalities for rough singular integral operators
Li, K.; Pérez, C.; Rivera-Ríos, I.P.; Roncal, L. (2018-08-17)
In this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals $T_\Omega$ with $\Omega\in L^\infty(\mathbb{S}^{n-1})$ and the Bochner--Riesz multiplier at the critical index ...