On existence of the weak solution for non-linear partial differential equations of elliptic type. II.
On extreme points of Orlicz spaces with Orlicz norm.
In the paper we consider a class of Orlicz spaces equipped with the Orlicz norm over a non-negative, complete and sigma-finite measure space (T,Sigma,mu), which covers, among others, Orlicz spaces isomorphic to L-infinite and the interpolation space L1 + L-infinite. We give some necessary conditions for a point x from the unit sphere to be extreme. Applying this characterization, in the case of an atomless measure mu, we find a description of the set of extreme points of L1 + L-infinite which corresponds...
On factorization of Fefferman's inequality
On Fourier coefficients and factorable operators.
On functions of bounded (p,2)-variation.
On functions of integrable mean oscillation.
On generalized Moser-Trudinger inequalities without boundary condition
We give a version of the Moser-Trudinger inequality without boundary condition for Orlicz-Sobolev spaces embedded into exponential and multiple exponential spaces. We also derive the Concentration-Compactness Alternative for this inequality. As an application of our Concentration-Compactness Alternative we prove that a functional with the sub-critical growth attains its maximum.
On generalized variations (II)
On global approximation properties of abstract integral operators in Orlicz spaces and applications.
On Hardy's inequality in .
On inequalities with measures of Sobolev type embedding theorems on open sets of the real axis.
On interpolation of weighted -spaces and Ovchinnikov’s theorem
On isometric domains of positive operators on -spaces
On isometric domains of positive operators on orlicz spaces
On isomorphisms of some Köthe function F-spaces
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...
On Jackson type inequality in Orlicz classes.
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.
On James and Jordan-von Neumann constants and the normal structure coefficient of Banach spaces
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.
On K-nearly uniform convexity in Orlicz spaces.
On L 1 Space Formed by Complex-Valued Partial Functions
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.
On L 1 Space Formed by Real-Valued Partial Functions
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...