The moduli of smoothness and convexity and the Rademacher averages of the trace classes (1≤p<∞)
The multiplication functions of Kučera
The multipliers of a space of almost convergent continuous functions
The Navier-Stokes equations in the critical Morrey-Campanato space.
The near-ring of Lipschitz functions on a metric space.
The Neumann problem for the Hénon equation, trace inequalities and Steklov eigenvalues
The non-archimedean Corona problem
The non-archimedean space
The non-archimedian space BC(X) with the strict topology.
Let X be a zero-dimensional, Hausdorff topological space and K a field with non-trivial, non-archimedean valuation under which it is complete. Then BC(X) is the vector space of the bounded continuous functions from X to K. We obtain necessary and sufficient conditions for BC(X), equipped with the strict topology, to be of countable type and to be nuclear in the non-archimedean sense.
The non-pluripolarity of compact sets in complex spaces and the property for the space of germs of holomorphic functions
The aim of this paper is to establish the equivalence between the non-pluripolarity of a compact set in a complex space and the property for the dual space of the space of germs of holomorphic functions on that compact set.
The Oka-Weil theorem in locally convex spaces with the approximation property
The One-Third-Trick and Shift Operators
We obtain a representation as martingale transform operators for the rearrangement and shift operators introduced by T. Figiel. The martingale transforms and the underlying sigma algebras are obtained explicitly by combinatorial means. The known norm estimates for those operators are a direct consequence of our representation.
The order topology for function lattices and realcompactness.
The Orthogonal Projection and the Riesz Representation Theorem
In this article, the orthogonal projection and the Riesz representation theorem are mainly formalized. In the first section, we defined the norm of elements on real Hilbert spaces, and defined Mizar functor RUSp2RNSp, real normed spaces as real Hilbert spaces. By this definition, we regarded sequences of real Hilbert spaces as sequences of real normed spaces, and proved some properties of real Hilbert spaces. Furthermore, we defined the continuity and the Lipschitz the continuity of functionals...
The Poisson's problem for the Laplacian with Robin boundary condition in non-smooth domains.
The positive cone of a Banach lattice. Coincidence of topologies and metrizability
Let be a Banach lattice, and denote by its positive cone. The weak topology on is metrizable if and only if it coincides with the strong topology if and only if is Banach-lattice isomorphic to for a set . The weak topology on is metrizable if and only if is Banach-lattice isomorphic to a -space, where is a metrizable compact space.
The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of
Let (S, ∑, m) be any atomless finite measure space, and X any Banach space containing a copy of . Then the Bochner space is uncomplemented in ccabv(∑,m;X), the Banach space of all m-continuous vector measures that are of bounded variation and have a relatively compact range; and ccabv(∑,m;X) is uncomplemented in cabv(∑,m;X). It is conjectured that this should generalize to all Banach spaces X without the Radon-Nikodym property.
The problem and singular integrals on Orlicz spaces
The Properties of the Weighted Space and Weighted Set
We study the properties of the weighted space and weighted set for boundary value problem with singularity.
The Property (DN) and the Exponential Representation of Holomorphic Functions.