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This paper is devoted to the study of the relatively compact sets in Quasi-Banach function spaces, providing an important improvement of the known results. As an application, we take the final step in establishing a relative compactness criteria for function spaces with any weight without any assumption.
In this paper we develop a stochastic integration theory for processes with values in a quasi-Banach space. The integrator is a cylindrical Brownian motion. The main results give sufficient conditions for stochastic integrability. They are natural ex
In this note, we show that the Hausdorff operator $H_{Phi}$ is unbounded on a large family of Quasi-Banach spaces, unless $H_{Phi}$ is a zero operator.
We develop a functional framework suitable for the treatment of partial differential equations and variational problems posed on evolving families of Banach spaces. We propose a definition for the weak time derivative which does not rely on the avail
The purpose of this note is to discuss how various Sobolev spaces defined on multiple cones behave with respect to density of smooth functions, interpolation and extension/restriction to/from $RR^n$. The analysis interestingly combines use of Poincar
Let $X$ be an infinite dimensional uniformly smooth Banach space. We prove that $X$ contains an infinite equilateral set. That is, there exists a constant $lambda>0$ and an infinite sequence $(x_i)_{i=1}^inftysubset X$ such that $|x_i-x_j|=lambda$ for all $i eq j$.