4 papers
On multiplier analogues of the algebra on weighted rearrangement-invariant sequence spaces
Oleksiy Karlovych, Sandra Mary Thampi
Let be a reflexive rearrangement-invariant Banach sequence space with nontrivial Boyd indices and let be a symmetric weight in the intersection of the…
On the essential norms of Toeplitz operators on abstract Hardy spaces built upon Banach function spaces
Oleksiy Karlovych, Eugene Shargorodsky
Let be a Banach function space over the unit circle such that the Riesz projection is bounded on and let be the abstract Hardy space built upon . We show that…
A necessary condition for the boundedness of the maximal operator on over reverse doubling spaces of homogeneous type
Oleksiy Karlovych, Alina Shalukhina
Let be a space of homogeneous type and be a variable exponent. We show that if the measure is Borel-semiregular and reverse doubling, then t…
Bounded compact and dual compact approximation properties of Hardy spaces: new results and open problems
Oleksiy Karlovych, Eugene Shargorodsky
The aim of the paper is to highlight some open problems concerning approximation properties of Hardy spaces. We also present some results on the bounded compact and the dual compac…