On relations approximated by continuous functions
On relatively disjoint families of measures, with some applications to Banach space theory
On restriction properties of multiplication operators.
On reverse Hardy's inequality.
On S. Mazur's problems 8 and 88 from the Scottish Book
The paper discusses Problems 8 and 88 posed by Stanisław Mazur in the Scottish Book. It turns out that negative solutions to both problems are immediate consequences of the results of Peller [J. Operator Theory 7 (1982)]. We discuss here some quantitative aspects of Problems 8 and 88 and give answers to open problems discussed in a recent paper of Pełczyński and Sukochev in connection with Problem 88.
On Schwartz's C-spaces and Orlicz's O-spaces
On sequential properties of Banach spaces, spaces of measures and densities
We show that a conjunction of Mazur and Gelfand-Phillips properties of a Banach space can be naturally expressed in terms of weak* continuity of seminorms on the unit ball of . We attempt to carry out a construction of a Banach space of the form which has the Mazur property but does not have the Gelfand-Phillips property. For this purpose we analyze the compact spaces on which all regular measures lie in the weak* sequential closure of atomic measures, and the set-theoretic properties of generalized...
On sequentially M-integrable distributions
On sharp reiteration theorems and weighted norm inequalities
We prove sharp end forms of Holmstedt's reiteration theorem which are closely connected with a general form of Gehring's Lemma. Reverse type conditions for the Hardy-Littlewood-Pólya order are considered and the maximal elements are shown to satisfy generalized Gehring conditions. The methods we use are elementary and based on variants of reverse Hardy inequalities for monotone functions.
On Simultaneous Extensions.
On Sobolev spaces of fractional order and ε-families of operators on spaces of homogeneous type
We introduce Sobolev spaces for 1 < p < ∞ and small positive α on spaces of homogeneous type as the classes of functions f in with fractional derivative of order α, , as introduced in [2], in . We show that for small α, coincides with the continuous version of the Triebel-Lizorkin space as defined by Y. S. Han and E. T. Sawyer in [4]. To prove this result we give a more general definition of ε-families of operators on spaces of homogeneous type, in which the identity operator is...
On solvability of fourth order operator-diferential equations of elliptic type on weight spaces.
On some basic relations in the abstract Hardy algebra theory
On some characterizations of Carleson type measure in the unit ball.
On some classes of function sequence spaces
On some classes of holomorphic vector functions
On some classes of infinitely decomposable Sobolev-Schwartz test functions
On some convexities of Orlicz and Orlicz-Bochner spaces
On some convexity properties in the Besicovitch-Musielak-Orlicz space of almost periodic functions with Luxemburg norm
In this article, it is shown that geometrical properties such as local uniform convexity, mid point local uniform convexity, H-property and uniform convexity in every direction are equivalent in the Besicovitch-Musielak-Orlicz space of almost periodic functions endowed with the Luxemburg norm.
On some convexity properties of Musielak-Orlicz spaces