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Stein-Weiss inequality in 𝐿¹ norm for vector fields

Publikováno v: Proceedings of the American Mathematical Society.

In this work, we investigate the limit case p = 1 p=1 of the classical Stein-Weiss inequality for the Riesz potential. Our main result is a characterization of this inequality for a special class of vector fields associated to cocanceling operators i

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::882c95cadb81569736756c5840b4a691
https://doi.org/10.1090/proc/16241

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On local continuous solvability of equations associated to elliptic and canceling linear differential operators

Autor: Laurent Moonens, Tiago Picon

Publikováno v: Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP

Consider A ( x , D ) : C ∞ ( Ω , E ) → C ∞ ( Ω , F ) an elliptic and canceling linear differential operator of order ν with smooth complex coefficients in Ω ⊂ R N from a finite dimension complex vector space E to a finite dimension comple

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https://doi.org/10.1016/j.matpur.2020.12.001

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On the Continuity and Compactness of Pseudodifferential Operators on Localizable Hardy Spaces

Autor: Tiago Picon, R. Kapp, G. Hoepfner

Publikováno v: Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP

In this paper we establish Sobolev type compact embedding theorems for Hormander classes of pseudodifferential operators $OpS^{-\alpha }_{1,\delta }$ on localizable Hardy space. Our work include new optimal boundedness results. As application, we obt

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::13ff00c338afa29f8268910f2d2dafde
https://doi.org/10.1007/s11118-020-09866-0

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Inhomogeneous cancellation conditions and Calderón–Zygmund type operators on hp

Autor: Galia Dafni, Chun Ho Lau, Tiago Picon, Claudio Vasconcelos

Publikováno v: Nonlinear Analysis. 225:113110

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::e91ee92181cef212b5a96372805764cc
https://doi.org/10.1016/j.na.2022.113110

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Local Hardy-Littlewood-Sobolev inequalities for canceling elliptic differential operators

Autor: Tiago Picon, Jorge Hounie

Publikováno v: Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP

Let A ( x , D ) be an elliptic linear differential operator of order ν with smooth complex coefficients in Ω ⊂ R N from a complex vector space E to a complex vector space F. In this paper we show that if l ∈ R satisfies 0 l N and l ≤ ν , the

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Solving the Equation

Autor: Tiago Picon, Laurent Moonens

Publikováno v: Proceedings of the Edinburgh Mathematical Society. 61:1055-1061

In the following note, we focus on the problem ofexistenceof continuous solutions vanishing at infinity to the equation divv = fforf ∈ Ln(ℝn) and satisfying an estimate of the type ||v||∞ ⩽ C||f||nfor anyf ∈ Ln(ℝn), whereC > 0 is related

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https://doi.org/10.1017/s0013091518000172

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L1 Sobolev estimates for (pseudo)-differential operators and applications

Autor: Jorge Hounie, Tiago Picon

Publikováno v: Mathematische Nachrichten. 289:1838-1854

In this work we show that if A(x,D) is a linear differential operator of order ν with smooth complex coefficients in Ω⊂RN from a complex vector space E to a complex vector space F, the Sobolev a priori estimate ∥u∥Wν−1,N/(N−1)≤C∥A(x,

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https://doi.org/10.1002/mana.201500017

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Regularity of maximal functions on Hardy-Sobolev spaces

Autor: Carlos Pérez, Mateus Sousa, Olli Saari, Tiago Picon

Publikováno v: Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP

We prove that maximal operators of convolution type associated to smooth kernels are bounded in the homogeneous Hardy-Sobolev spaces $\dot{H}^{1,p}(\mathbb{R}^d)$ when $1/p < 1+1/d$. This range of exponents is sharp. As a by-product of the proof, we

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$$L^1$$ L 1 – $$L^p$$ L p estimates for radial solutions of the wave equation and application

Autor: R. Kapp, Marcelo R. Ebert, Tiago Picon

Publikováno v: Annali di Matematica Pura ed Applicata (1923 -). 195:1081-1091

It is well known that, for space dimension $n> 3$, one cannot generally expect $L^1$–$L^p$ estimates for the solution of $$\begin{aligned} u_{tt}-\varDelta u = 0, \quad u(0,x)=0,\quad u_t(0,x)=g(x), \end{aligned}$$ where \((t,x)\in {\mathbb {

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https://doi.org/10.1007/s10231-015-0505-z

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