A note on the isomorphic classification of spaces of continuous functions defined on intervals of ordinal numbers
A note on the Köthe dual of Banach-valued echelon spaces.
A note on the paper “The Poulsen Simplex” of Lindenstrauss, Olsen and Sternfeld
It is proved that for any , where is the Poulsen simplex, so that and , are smooth points, there is a rotation of carrying in .
A note on the Poincaré inequality
The Poincaré inequality is extended to uniformly doubling metric-measure spaces which satisfy a version of the triangle comparison property. The proof is based on a generalization of the change of variables formula.
A note on the predual of Lip(S, d)
A note on Toeplitz operators on Bergman spaces
A note on wavelet bases in function spaces
A Note on Weighten Integrals of Analytic Functions
A notion of Orlicz spaces for vector valued functions
The notion of the Orlicz space is generalized to spaces of Banach-space valued functions. A well-known generalization is based on -functions of a real variable. We consider a more general setting based on spaces generated by convex functions defined on a Banach space. We investigate structural properties of these spaces, such as the role of the delta-growth conditions, separability, the closure of , and representations of the dual space.
A one-dimensional nonlinear degenerate elliptic equation.
A pair of linear functional inequalities and a characterization of -norm
It is shown that, under some general algebraic conditions on fixed real numbers a,b,α,β, every solution f:ℝ → ℝ of the system of functional inequalities f(x+a) ≤ f(x)+α, f(x+b) ≤ f(x)+β that is continuous at some point must be a linear function (up to an additive constant). Analogous results for three other similar simultaneous systems are presented. An application to a characterization of -norm is given.
A Positive Compact Operator.
A potential operator and some ergodic properties of a positive contraction
A priori estimate for a system of differential operators.
A priori estimates in geometry and Sobolev spaces on open manifolds
Introduction. For bounded domains in satisfying the cone condition there are many embedding and module structure theorem for Sobolev spaces which are of great importance in solving partial differential equations. Unfortunately, most of them are wrong on arbitrary unbounded domains or on open manifolds. On the other hand, just these theorems play a decisive role in foundations of nonlinear analysis on open manifolds and in solving partial differential equations. This was pointed out by the author...
A priori inequalities in for solutions of elliptic equations in unbounded domains
A problem about set translations on the real line
A property of multiplication in Sobolev spaces. Some applications
A quasi-dichotomy for C(α,X) spaces, α < ω₁
We prove the following quasi-dichotomy involving the Banach spaces C(α,X) of all X-valued continuous functions defined on the interval [0,α] of ordinals and endowed with the supremum norm. Suppose that X and Y are arbitrary Banach spaces of finite cotype. Then at least one of the following statements is true. (1) There exists a finite ordinal n such that either C(n,X) contains a copy of Y, or C(n,Y) contains a copy of X. (2) For any infinite countable...
-condition for two weight functions and compact imbeddings of weighted Sobolev spaces