Carleson measure problems for parabolic Bergman spaces and homogeneous Sobolev spaces
نویسندگان
چکیده
منابع مشابه
Carleson Measure Problems for Parabolic Bergman Spaces and Homogeneous Sobolev Spaces
Let bα(R 1+n + ) be the space of solutions to the parabolic equation ∂tu+ (−△)u = 0 (α ∈ (0, 1]) having finite L(R 1+n + ) norm. We characterize nonnegative Radon measures μ on R + having the property ‖u‖Lq(R1+n + ,μ) . ‖u‖ Ẇ1,p(R + ) , 1 ≤ p ≤ q < ∞, whenever u(t, x) ∈ bα(R 1+n + ) ∩ Ẇ 1.p(R + ). Meanwhile, denoting by v(t, x) the solution of the above equation with Cauchy data v0(x), we chara...
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ژورنال
عنوان ژورنال: Nonlinear Analysis: Theory, Methods & Applications
سال: 2010
ISSN: 0362-546X
DOI: 10.1016/j.na.2010.06.040