In this paper, we introduce some new classes of functions and investigate the embedding relations among these classes. Our results generalize the related results of Leindler [3] and Yu-Zhou [9].
In this paper, we establish strong embedding theorems, in the sense of the Komlós-Major-Tusnády framework, for the performance metrics of a general class of transitory queueing models of nonstationary queueing systems. The nonstationary and non-Markovian nature of these models makes the computation of performance metrics hard. The strong embeddings yield error bounds on sample path approximations by diffusion processes in the form of functional strong approximation theorems.
This chapter presents a selection of some of the most important results in the theory of Sobolev spacesn. Special emphasis is placed on embedding theorems and the question as to whether an embedding map is compact or not. Some results concerning the k-set contraction nature of certain embedding maps are given, for both bounded and unbounded space domains: also the approximation numbers of embedding maps are estimated and these estimates used to classify the embeddings.
AbstractWe establish an embedding theorem for the weighted Bergman spaces induced by a positive Borel measure $$d\omega (y)dx$$
d
ω
(
y
)
d
x
with the doubling property $$\omega (0,2t)\le C\omega (0,t)$$
ω
(
0
,
2
t
)
≤
C
ω
(
0
,
t
)
. The characterization is given in terms of Carleson squares on the upper half-plane. As special cases, our result covers the standard weights and logarithmic weights. As an application, we also establish the boundedness of the area operator.
A note on strong approximation of Fourier series and embedding theorems
