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+34 946 567 842
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+34 946 567 842
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cperez@bcamath.org
Information of interest
My research is mainly focused in the area of Real and Harmonic Analysis. More recently I have been interested in the deep connection between the operator norm of some of the basic operators from Harmonic Analysis such as the Calderón-Zygmund operators, its commutators or maximal functions with the growth of the Ap constants in different various natural spaces. I am also particularly interested in other deep aspects of the theory such as the extrapolation theory and the Reverse Hölder property of the Ap class of weights. I also consider multilinear aspects of the Calderón-Zygmund theory where many questions are still open. Another good portion of my research interest is related to the theory of multiparameter Harmonic Analysis and its interplay with the theory of weights.
I also like to explore the connection with questions coming from the theory of Schrödinger operators and (degenerate) Poincaré-Sobolev inequalities.
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WEIGHTED FRACTIONAL POINCARE ́ INEQUALITIES VIA ISOPERIMETRIC INEQUALITIES
Pérez, C.
; Weigt, J.; Myyryläinen, K. (2024)
Our main result is a weighted fractional Poincar ́e–Sobolev inequality improving the celebrated estimate by Bourgain–Brezis–Mironescu. This also yields an improvement of the classical Meyers–Ziemer theorem in several ways. ...
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A TRIBUTE TO POLA HARBOURE: ISOPERIMETRIC INEQUALITIES AND THE HMS EXTRAPOLATION THEOREM
Pérez, C.; Rela, E. (2023)
We give a different simpler proof of the Gagliardo estimate with a measure obtained in [FPW00] and improved in [PR19]. This result will be further improved using fractional Poincaré type inequalities with the extra bonus ...
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Remarks on vector-valued Gagliardo and Poincar ́e-Sobolev type inequalities with weights
Pérez, C.; Martínez-Perales, J. (2023)
In this paper we review certain extensions of the Gagliardo and Poincar ́e-Sobolev type inequalities to later explore the possibility of extending them to the vector-valued setting. We restrict ourselves to the most classical ...
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AN HOMAGE TO GUIDO WEISS AND HIS LEADERSHIP OF THE SAINT LOUIS TEAM: COMMUTATORS OF SINGULAR INTEGRALS AND SOBOLEV INEQUALITIES
Hoang, C.; Moen, K.; Pérez, C. (2023)
We extend some classical Sobolev type inequalities for linear and non-linear commutators.
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WEIGHTED LORENTZ SPACES: SHARP MIXED Ap − A∞ ESTIMATE FOR MAXIMAL FUNCTIONS
Accomazzo, N.; Duoandikoetxea, J.; Nieraeth, Z.; Ombrosi, S.; Pérez, C. (2023)
We prove the sharp mixed Ap − A∞ weighted estimate for the Hardy-Littlewood maximal function in the context of weighted Lorentz spaces, namely 11 ∥M∥ p,q ≲p,q,n [w]p [σ]min(p,q) , L (w) Ap A∞ 1 where σ = w 1−p . Our ...
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ON THE WEIGHTED INEQUALITY BETWEEN THE GAGLIARDO AND SOBOLEV SEMINORMS
Pérez, C.; Martínez-Perales, J.; Hurri-Syrjänen, R.; Vähäkangas, A.V. (2023)
We prove weighted inequalities between the Gagliardo and Sobolev seminorms. With A1 weights we improve earlier results of Bourgain, Brezis, and Mironescu.
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POINTWISE ESTIMATES FOR ROUGH OPERATORS WITH APPLICATIONS TO SOBOLEV INEQUALITIES
Hoang, C.; Moen, K.; Pérez, C. (2023)
We investigate weighted Sobolev inequalities for rough operators. We prove that several operators satisfy a pointwise bound by the Riesz potential applied to the gradient. From this inequality, we derive several new Sobolev ...
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Sawyer-type inequalities for Lorentz spaces
Pérez, C.; Roure-Perdices, E. (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. ...
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On the BBM-Phenomenon in Fractional Poincaré–Sobolev Inequalities with Weights
Hurri-Syrjänen, R.; Martinez-Perales, J.C.; Pérez, C.; Vähäkangas, A.V. (2022)
In this paper, we unify and improve some of the results of Bourgain, Brezis, and Mironescu and the weighted Poincaré–Sobolev estimate by Fabes, Kenig, and Serapioni. More precisely, we get weighted counterparts of the ...
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Some Non-standard Biparametric Poincaré Type Inequalities Through Harmonic Analysis
Cejas, M.E.; Mosquera, C.; Pérez, C.; Rela, E. (2022)
We show some non-standard Poincaré type estimates in the biparametric setting with appropriate weights. We will derive these results using variants from classical estimates exploiting the interplay between maximal functions ...
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Minimal conditions for BMO
Canto, J.; Pérez, C.; Rela, E. (2022)
We study minimal integrability conditions via Luxemburg- type expressions with respect to generalized oscillations that imply the membership of a given function f to the space BMO. Our method is simple, sharp and flexible ...
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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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SELF-IMPROVING POINCARE ́-SOBOLEV TYPE FUNCTIONALS IN PRODUCT SPACES
Pérez, C.; Cejas, M.E.; Mosquera, C.; Rela, E. (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 L1 norms in the context of product spaces. The ...
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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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$A_1$ 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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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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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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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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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 ...
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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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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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$A_1$ 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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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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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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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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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].