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Resultats globals: 7 registres trobats en 0.03 segons.
Articles, 6 registres trobats
Documents de recerca, 1 registres trobats
Articles 6 registres trobats  
1.
32 p, 706.4 KB An α-number characterization of Lp spaces on uniformly rectifiable sets / Azzam, Jonas (University of Edinburgh. School of Mathematics) ; Dąbrowski, Damian (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We give a characterization of Lp(σ) for uniformly rectifiable measures σ using Tolsa's α-numbers, by showing, for 1 < p < ∞ and f ∈ Lp(σ), that kfkLp(σ) ∼Z ∞0(αfσ(x, r) + |f|x,rασ(x, r))2drr12Lp(σ).
2023 - 10.5565/PUBLMAT6722313
Publicacions matemàtiques, Vol. 67 Núm. 2 (2023) , p. 819-850 (Articles)  
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2.
77 p, 1.1 MB Gradient of the single layer potential and quantitative rectifiability for general Radon measures / Puliatti, Carmelo (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We identify a set of sufficient local conditions under which a significant portion of a Radon measure μ on with compact support can be covered by an uniformly n-rectifiable set, at the level of a ball such that . [...]
2022 - 10.1016/j.jfa.2021.109376
Journal of Functional Analysis, Vol. 282, Issue 6 (March 2022) , art. 109376  
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3.
29 p, 479.8 KB Rectifiability of measures and the βp coefficients / Tolsa Domènech, Xavier (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In some former works of Azzam and Tolsa it was shown that n-rectifiabilitycan be characterized in terms of a square function involving the David-Semmes β2 coecients. In the present paper we construct some counterexamples which show that a similar characterization does not hold for the βp coefficients with p = 2. [...]
2019 - 10.5565/PUBLMAT6321904
Publicacions matemàtiques, Vol. 63 Núm. 2 (2019) , p. 491-519 (Articles)  
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4.
16 p, 424.3 KB Tangents, rectifiability, and corkscrew domains / Azzam, Jonas (University of Edinburgh. School of Mathematics)
In a recent paper, Csörnyei and Wilson prove that curves in Euclidean space of σ-finite length have tangents on a set of positive H 1-measure. They also show that a higher dimensional analogue of this result is not possible without some additional assumptions. [...]
2018 - 10.5565/PUBLMAT6211808
Publicacions matemàtiques, Vol. 62 Núm. 1 (2018) , p. 161-176 (Articles)  
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5.
16 p, 405.7 KB The Riesz transform, rectifiability, and removability for Lipschitz harmonic functions / Nazarov, Fedor (Kent State University. Department of Mathematical Sciences) ; Tolsa Domènech, Xavier (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Volberg, Alexander (Michigan State University. Department of Mathematics)
We show that, given a set E Rn+1 with finite n-Hausdorff measure Hn, if the n-dimensional Riesz transform is bounded in L2(HnbE), then E is n-rectifiable. From this result we deduce that a compact set E Rn+1 with Hn(E) < 1 is removable for Lipschitz harmonic functions if and only if it is purely n-unrectifiable, thus proving the analog of Vitushkin's conjecture in higher dimensions.
2014 - 10.5565/PUBLMAT_58214_26
Publicacions matemàtiques, Vol. 58, Núm. 2 (2014) , p. 517-532  
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6.
31 p, 287.8 KB Finite curvature of arc length measure implies rectifiability : a new proof / Tolsa Domènech, Xavier (Institució Catalana de Recerca i Estudis Avançats)
If E C C is a set with finite length and finite curvature, then E is rectifiable. This fact, proved by David and Léger in 1999, is one of the basic ingredients for the proof of Vitushkin's conjecture. [...]
2005 - 10.1512/iumj.2005.54.2746
Indiana University mathematics journal, Vol. 54, No. 4 (2005) , p. 1075-1105  
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Documents de recerca 1 registres trobats  
1.
246 p, 1.7 MB Rectifiability of Radon measures / Dąbrowski, Damian ; Tolsa Domènech, Xavier, dir. ; Universitat Autònoma de Barcelona. Departament de Matemàtiques
Aquesta tesi es dedica a l'estudi de mesures rectificables, de rectificabilitat quantitativa i, en menor grau, del límit dels operadors integrals singulars definits respecte a mesures amb creixement polinòmic.
Esta tesis está dedicada al estudio de medidas rectificables, rectificabilidad cuantitativa y, en menor grado, la acotación de operadores integrales singulares definidos respecto a medidas con crecimiento polinomial.
This thesis is dedicated to the study of rectifiable measures, quantitative rectifiability, and to a lesser degree, the boundedness of singular integral operators defined with respect to measures with polynomial growth.
2021  
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