Carlos Pérez Moreno

Group Leader. BCAM - UPV/EHU Ikerbasque Research Professor

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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.  

  • Sawyer-type inequalities for Lorentz spaces 

    Pérez, C.Autoridad BCAM; 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. ...
  • Degenerate Poincare-Sobolev inequalities 

    Pérez, C.Autoridad BCAM; 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 ...
  • Extensions of the John-Nirenberg theorem and applications 

    Canto, J.Autoridad BCAM; Pérez, C.Autoridad BCAM (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 

    Cejas, M.E.; Mosquera, C.; Pérez, C.Autoridad BCAM; 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 L 1 norms in the context of product spaces. ...
  • A note on generalized Fujii-Wilson conditions and BMO spaces 

    Ombrosi, S.; Pérez, C.Autoridad BCAM; 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. ...
  • Regularity of maximal functions on Hardy–Sobolev spaces 

    Pérez, C.Autoridad BCAM; 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 ...
  • Weighted norm inequalities for rough singular integral operators 

    Li, K.; Pérez, C.Autoridad BCAM; Rivera-Ríos, I.P.; Roncal, L.Autoridad BCAM (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 ...
  • Borderline Weighted Estimates for Commutators of Singular Integrals 

    Pérez, C.Autoridad BCAM; 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 ...
  • A note on the off-diagonal Muckenhoupt-Wheeden conjecture 

    Cruz-Uribe, D.; Martell, J.M.; Pérez, C.Autoridad BCAM (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 ...
  • Reverse Hölder Property for Strong Weights and General Measures 

    Luque, T.; Pérez, C.Autoridad BCAM; 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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