{"id":46,"date":"2013-11-08T11:00:54","date_gmt":"2013-11-08T09:00:54","guid":{"rendered":"http:\/\/mat.uab.cat\/~jvm\/?page_id=46"},"modified":"2023-09-26T14:47:29","modified_gmt":"2023-09-26T12:47:29","slug":"papers","status":"publish","type":"page","link":"https:\/\/mat.uab.cat\/web\/jvm\/papers\/","title":{"rendered":"RESEARCH PAPERS"},"content":{"rendered":"
<\/a><\/form>

2023<\/h3>

J. Cuf\u00ed, J.J. Donaire, P. Mattila, J. Verdera<\/p>

Existence of Principal Values of some singular Integrals on Cantor sets, and Hausdorff dimension<\/a> Journal Article<\/span> <\/p>

In: <\/span>Pacific Journal Of Mathematics, <\/span>vol. 326, <\/span>no. 2, <\/span>pp. 285-300, <\/span>2023<\/span>.<\/p>

Abstract<\/a><\/span> | Links<\/a><\/span> | BibTeX<\/a><\/span><\/p>

@article{nokey,
\r\ntitle = {Existence of Principal Values of some singular Integrals on Cantor sets, and Hausdorff dimension},
\r\nauthor = {J. Cuf\\'{i}, J.J. Donaire, P. Mattila, J. Verdera},
\r\nurl = {http:\/\/mat.uab.cat\/web\/jvm\/wp-content\/uploads\/sites\/35\/2024\/01\/Pacific_3262_2023_285_300.pdf},
\r\ndoi = {https:\/\/doi.org\/10.2140\/pjm.2023.326.285},
\r\nyear  = {2023},
\r\ndate = {2023-12-31},
\r\nurldate = {2023-12-01},
\r\njournal = {Pacific Journal Of Mathematics},
\r\nvolume = {326},
\r\nnumber = {2},
\r\npages = {285-300},
\r\nabstract = {Consider a standard Cantor set in the plane of Hausdorff dimension 1. If
\r\nthe linear density of the associated measure \u03bc vanishes, then the set of
\r\npoints where the principal value of the Cauchy singular integral of \u03bc exists
\r\nhas Hausdorff dimension 1. The result is extended to Cantor sets in Rd of
\r\nHausdorff dimension \u03b1 and Riesz singular integrals of homogeneity \u2212\u03b1,
\r\n0 \\< \u03b1 \\< d: the set of points where the principal value of the Riesz singular
\r\nintegral of \u03bc exists has Hausdorff dimension \u03b1. A martingale associated with
\r\nthe singular integral is introduced to support the proof.},
\r\nkeywords = {},
\r\npubstate = {published},
\r\ntppubtype = {article}
\r\n}
\r\n<\/pre><\/div>
Close<\/a><\/p><\/div>
Consider a standard Cantor set in the plane of Hausdorff dimension 1. If
\r\nthe linear density of the associated measure \u03bc vanishes, then the set of
\r\npoints where the principal value of the Cauchy singular integral of \u03bc exists
\r\nhas Hausdorff dimension 1. The result is extended to Cantor sets in Rd of
\r\nHausdorff dimension \u03b1 and Riesz singular integrals of homogeneity \u2212\u03b1,
\r\n0 < \u03b1 < d: the set of points where the principal value of the Riesz singular
\r\nintegral of \u03bc exists has Hausdorff dimension \u03b1. A martingale associated with
\r\nthe singular integral is introduced to support the proof.<\/div>
Close<\/a><\/p><\/div>