Carleson measure problems for parabolic Bergman spaces and homogeneous Sobolev spaces
| dc.creator | Zhai, Zhichun | |
| dc.date | 2009-04-21 | |
| dc.date.accessioned | 2026-07-07T13:06:54Z | |
| dc.date.available | 2026-07-07T13:06:54Z | |
| dc.description | Let $b_α^{p}(\mathbb{R}^{1+n}_{+})$ be the space of solutions to the parabolic equation $\partial_{t}u+(-\triangle)^αu=0$ $(α\in(0, 1])$ having finite $L^{p}(\mathbb{R}^{1+n}_{+})$ norm. We characterize nonnegative Radon measures $μ$ on $\mathbb{R}^{1+n}_{+}$ having the property $\|u\|_{L^{q}(\mathbb{R}^{1+n}_{+},μ)}\lesssim \|u\|_{\dot{W}^{1,p}(\mathbb{R}^{1+n}_{+})},$ $1\leq p\leq q<\infty,$ whenever $u(t,x)\in b_α^{p}(\mathbb{R}^{1+n}_{+})\cap \dot{W}^{1.p}(\mathbb{R}^{1+n}_{+}).$ Meanwhile, denoting by $v(t,x)$ the solution of the above equation with Cauchy data $v_{0}(x),$ we characterize nonnegative Radon measures $μ$ on $\mathbb{R}_{+}^{1+n}$ satisfying $\|v(t^{2α},x)\|_{L^{q}(\mathbb{R}_{+}^{1+n}, μ)}\lesssim\|v_{0}\|_{\dot{W}^{β,p}(\mathbb{R}^{n})},$ $β\in (0,n),$ $p\in [1, n/β],$ $q\in(0, \infty).$ Moreover, we obtain the decay of $v(t,x),$ an iso$-$capacitary inequality and a trace inequality. | |
| dc.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/0904.3287 | |
| dc.identifier | http://arxiv.org/abs/0904.3287 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/227926 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Carleson measure problems for parabolic Bergman spaces and homogeneous Sobolev spaces | |
| dc.type | text |