Riesz transforms of non-integer homogeneity on uniformly disconnected sets

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Riesz transforms of non-integer homogeneity on uniformly disconnected sets. / Reguera, Maria Carmen; Tolsa, Xavier.

In: Transactions of the American Mathematical Society, Vol. 368, No. 10, 10.2016, p. 7045–7095.

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@article{3ac5e8efe445432ca81bec16c69d59f3,
title = "Riesz transforms of non-integer homogeneity on uniformly disconnected sets",
abstract = "In this paper we obtain precise estimates for the L2 norm of the s-dimensional Riesz transforms on very general measures supported on Cantor sets in Rd, with d − 1 <s<d. From these estimates we infer that, for the so-called uniformly disconnected compact sets, the capacity γs associated with the Riesz kernel x/|x| s+1 is comparable to the capacity C˙ 2 3 (d−s), 3 2 from non-linear potential theory.",
keywords = "math.CA, math.AP",
author = "Reguera, {Maria Carmen} and Xavier Tolsa",
note = "Minor corrections",
year = "2016",
month = oct,
doi = "10.1090/tran/6587",
language = "English",
volume = "368",
pages = "7045–7095",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "10",

}

RIS

TY - JOUR

T1 - Riesz transforms of non-integer homogeneity on uniformly disconnected sets

AU - Reguera, Maria Carmen

AU - Tolsa, Xavier

N1 - Minor corrections

PY - 2016/10

Y1 - 2016/10

N2 - In this paper we obtain precise estimates for the L2 norm of the s-dimensional Riesz transforms on very general measures supported on Cantor sets in Rd, with d − 1 <s<d. From these estimates we infer that, for the so-called uniformly disconnected compact sets, the capacity γs associated with the Riesz kernel x/|x| s+1 is comparable to the capacity C˙ 2 3 (d−s), 3 2 from non-linear potential theory.

AB - In this paper we obtain precise estimates for the L2 norm of the s-dimensional Riesz transforms on very general measures supported on Cantor sets in Rd, with d − 1 <s<d. From these estimates we infer that, for the so-called uniformly disconnected compact sets, the capacity γs associated with the Riesz kernel x/|x| s+1 is comparable to the capacity C˙ 2 3 (d−s), 3 2 from non-linear potential theory.

KW - math.CA

KW - math.AP

U2 - 10.1090/tran/6587

DO - 10.1090/tran/6587

M3 - Article

VL - 368

SP - 7045

EP - 7095

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 10

ER -