PARABOLIC COMPACTIFICATION OF HOMOGENEOUS SPACES

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...

Frames and Homogeneous Spaces

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

Convolution and Homogeneous Spaces

Nagata Compactification for Algebraic Spaces

We prove the Nagata compactification theorem for any separated map of finite type between quasi-compact and quasi-separated algebraic spaces, generalizing earlier results of Raoult. Along the way we also prove (and use) absolute noetherian approximation for such algebraic spaces, generalizing earlier results in the case of schemes. To the memory of Masayoshi Nagata

Compactification of -spaces Revisited Compactiication of G{spaces Revisited

We discuss compactiications of G{spaces from a new point of view that completely diiers from our earlier approaches. From a topologist's point of view, this new approach is more natural than the previous ones. In addition, it enables a uniied discussion of the compactiication and the linearization problem for G{spaces (which we shall discuss in a subsequent report). The central idea is to get a...