https://scholars.lib.ntu.edu.tw/handle/123456789/624589
標題: | The two weight T1 theorem for fractional Riesz transforms when one measure is supported on a curve | 作者: | Sawyer E.T CHUN-YEN SHEN Uriarte-Tuero I. |
公開日期: | 2020 | 卷: | 142 | 期: | 2 | 起(迄)頁: | 453-520 | 來源出版物: | Journal d'Analyse Mathematique | 摘要: | Let σ and ω be locally finite positive Borel measures on ℝn. We assume that at least one of the two measures σ and ω is supported on a regular C1,δ curve in ℝn. Let Rα,n be the α-fractional Riesz transform vector on ℝn. We prove the T1 theorem for Rα,n: namely that Rα,n is bounded from L2(σ) to L2(σ) if and only if the A2α conditions with holes hold, the punctured A2α conditions hold, and the cube testing condition for Rα,n and its dual both hold. The special case of the Cauchy transform, n = 2 and α = 1, when the curve is a line or circle, was established by Lacey, Sawyer, Shen, Uriarte-Tuero and Wick in [LaSaShUrWi]. This T1 theorem represents essentially the most general T1 theorem obtainable by methods of energy reversal. More precisely, for the pushforwards of the measures σ and ω, under a change of variable to straighten out the curve to a line, we use reversal of energy to prove that the quasienergy conditions in [SaShUr7] are implied by the A2α with holes, punctured A2α, and quasicube testing conditions for Rα,n. Then we apply the main theorem in [SaShUr7] to deduce the T1 theorem above. © 2020, The Hebrew University of Jerusalem. |
URI: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85099832855&doi=10.1007%2fs11854-020-0141-4&partnerID=40&md5=c42f10270d56e13d562488142d828275 https://scholars.lib.ntu.edu.tw/handle/123456789/624589 |
ISSN: | 00217670 | DOI: | 10.1007/s11854-020-0141-4 |
顯示於: | 數學系 |
在 IR 系統中的文件,除了特別指名其著作權條款之外,均受到著作權保護,並且保留所有的權利。