Using the Il'in integral representation of functions, imbedding theorems for weighted anisotropic Sobolev spaces in 𝔼ⁿ are proved. By the weight we assume a power function of the distance from an (n-2)-dimensional subspace passing through the domain considered.
The main goal of the paper is to formulate some new properties of the Ishlinskii hysteresis operator , which characterizes e.g. the relation between the deformation and the stress in a non-perfectly elastic (elastico-plastic) material. We introduce two energy functionals and derive the energy inequalities. As an example we investigate the equation describing the motion of a mass point at the extremity of an elastico-plastic spring.
We provide a complete isomorphic classification of the Banach spaces of continuous functions on the compact spaces , the topological sums of Cantor cubes , with smaller than the first sequential cardinal, and intervals of ordinal numbers [0,α]. In particular, we prove that it is relatively consistent with ZFC that the only isomorphism classes of spaces with ≥ ℵ₀ and α ≥ ω₁ are the trivial ones. This result leads to some elementary questions on large cardinals.
We prove that if Köthe F-spaces X and Y on finite atomless measure spaces (ΩX; ΣX, µX) and (ΩY; ΣY; µY), respectively, with absolute continuous norms are isomorphic and have the property (for µ = µX and µ = µY, respectively) then the measure spaces (ΩX; ΣX; µX) and (ΩY; ΣY; µY) are isomorphic, up to some positive multiples. This theorem extends a result of A. Plichko and M. Popov concerning isomorphic classification of L p(µ)-spaces for 0 < p < 1. We also provide a new class of F-spaces...
It is shown that Jackson type inequality fails in the Orlicz classes φ(L) if φ(x) differs essentially from a power function of any order.
Some relations between the James (or non-square) constant J(X) and the Jordan-von Neumann constant , and the normal structure coefficient N(X) of Banach spaces X are investigated. Relations between J(X) and J(X*) are given as an answer to a problem of Gao and Lau [16]. Connections between and J(X) are also shown. The normal structure coefficient of a Banach space is estimated by the -constant, which implies that a Banach space with -constant less than 5/4 has the fixed point property.
In this article, we formalized L1 space formed by complexvalued partial functions [11], [15]. The real-valued case was formalized in [22] and this article is its generalization.
This article contains some definitions and properties refering to function spaces formed by partial functions defined over a measurable space. We formalized a function space, the so-called L1 space and proved that the space turns out to be a normed space. The formalization of a real function space was given in [16]. The set of all function forms additive group. Here addition is defined by point-wise addition of two functions. However it is not true for partial functions. The set of partial functions...