Fractional Sobolev spaces, also known as Besov or Slobodetzki spaces, arise in many areas of analysis, stochastic analysis in particular. We prove an embedding into certain q-variation spaces and discuss a few applications. First we show q-variation regularity of Cameron-Martin paths associated to fractional Brownian motion and other Volterra processes. This is useful, for instance, to establis...

Around 1987 a German mathematician named Matthias Gunther found a new way of obtaining the existence of isometric embeddings of a Riemannian manifold. His proof appeared in [1, 2]. His approach avoids the so-called Nash-Moser iteration scheme and, therefore, the need to prove smooth tame or Moser-type estimates for the inverse of the linearized operator. This simplifies the proof of Nash’s isom...

In this paper we embed the space of upper semicontinuous convex fuzzy sets on a Banach space into a space of continuous functions on a compact space. The following structures are preserved by the embedding: convex cone, metric, sup-semilattice. The indicator function of the unit ball is mapped to the constant function 1. Two applications are presented: strong laws of large numbers for fuzzy ran...

In this paper we establish an L∞-bound for the Neumann problem of the Poisson equations. We first develop some estimates for the bounds of solutions in several spaces using Poincarés inequality, Trace theorem and Sobolev’s embedding theorem, and then prove our main theorem utilizing the De Giorgi-Nash estimates.

Theorem 1.1(1) improves on the previously best known result ([1]) by 1 dimension, while Theorem 1.1(2) improves on the previously best known nonimmersion and nonembedding results ([2]) for P 16n+10 and P 16n+11 by 4 dimensions, and is within 1 of best possible for them. It also implies new nonimmersions for P , P , and P . Theorem 1.2 improves on the previously best known embedding ([11]) of P ...

We characterize embeddability of algebraic varieties into smooth toric varieties and prevarieties. Our embedding results hold also in an equivariant context and thus generalize a well-known embedding theorem of Sumihiro on quasiprojective G-varieties. The main idea is to reduce the embedding problem to the affine case. This is done by constructing equivariant affine conoids, a tool which extend...

‎It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$‎. ‎Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology‎, ‎which is compact by the Banach--Alaoglu theorem‎. ‎We prove that the compact Hausdorff space $X$ can ...

It is shown that certain known integral inequalities imply directly a well-known embedding theorem of Besov spaces.