A modulation invariant Carleson embedding theorem outside local L2
A modulation invariant Carleson embedding theorem outside local L2
复制标题
局部L2外的调制不变Carleson嵌入定理
DOI：
10.1007/s11854-018-0049-4
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Yumeng Ou
中科院分区：
文献类型：
--
作者：
Francesco Di Plinio;Yumeng Ou
Yen Do and Christoph Thiele developed a theory of Carleson embeddings in outer Lp spaces for the wave packet transform $${F_\phi }(f)(u,t,\eta ) = \int {f(x){e^{i\eta (u - x)}}\phi \left( {\frac{{u - x}}{t}} \right)} \frac{{dx}}{t},(u,t,\eta ) \in R \times (0,\infty ) \times R$$Fϕ(f)(u,t,η)=∫f(x)eiη(u−x)ϕ(u−xt)dxt,(u,t,η)∈R×(0,∞)×R of functions f ∈ Lp(R) in the range 2 ≤ p ≤ ∞, referred to as local L2. In this article, we formulate a suitable extension of this theory to exponents 1 < p < 2, answering a question posed by Do and Thiele. The proof of our main embedding theorem involves a refined multi-frequency Calderón-Zygmund decomposition in the vein of work by Di Plinio and Thiele and by Nazarov, Oberlin, and Thiele. We apply our embedding theorem to recover the full known range of Lp estimates for the bilinear Hilbert transforms without reducing to discrete model sums or appealing to generalized restricted weak-type interpolation.
Yen Do and Christoph Thiele developed a theory of Carleson embeddings in outer Lp spaces for the wave packet transform $${F_\phi }(f)(u,t,\eta ) = \int {f(x){e^{i\eta (u - x)}}\phi \left( {\frac{{u - x}}{t}} \right)} \frac{{dx}}{t},(u,t,\eta ) \in R \times (0,\infty ) \times R$$Fϕ(f)(u,t,η)=∫f(x)eiη(u−x)ϕ(u−xt)dxt,(u,t,η)∈R×(0,∞)×R of functions f ∈ Lp(R) in the range 2 ≤ p ≤ ∞, referred to as local L2. In this article, we formulate a suitable extension of this theory to exponents 1 < p < 2, answering a question posed by Do and Thiele. The proof of our main embedding theorem involves a refined multi-frequency Calderón-Zygmund decomposition in the vein of work by Di Plinio and Thiele and by Nazarov, Oberlin, and Thiele. We apply our embedding theorem to recover the full known range of Lp estimates for the bilinear Hilbert transforms without reducing to discrete model sums or appealing to generalized restricted weak-type interpolation.
外测度的 Lp 理论与 Lennart Carleson 的两个主题相结合
DOI：
10.1090/s0273-0979-2014-01474-0
发表时间：
2015
期刊：
arXiv: Classical Analysis and ODEs
影响因子：
--
作者：
C. Thiele
通讯作者：
C. Thiele