We study the weak and strong type boundedness of maximal heat–diffusion operators associated with the system of generalized Hermite polynomials and with two different systems of generalized Hermite functions. We also give a necessary background to define Sobolev spaces in this context.

As a variation on the known theme of Gödel numberings, isomorphisms defining data type transformations in a strongly typed functional language are organized as a finite groupoid using a higher order combinator language that unifies popular data types as diverse as natural numbers, finite sequences, digraphs, hypergraphs and finite permutations with more exotic ones like hereditarily finite func...

In this paper generic software development steps of diierent complexity are represented and veriied using the (higher-order, strongly typed) speciication and veriication system PVS. The transformations considered in this paper include \large" powerful steps encoding general algorithmic paradigms as well as \smaller" transformations for the operationalization of a descriptive speciication. The a...

Abstract. The purpose of this paper is to prove strong type inequalities with one-sided weights for commutators (with symbol b ∈ BMO) of several one-sided operators, such as the one-sided discrete square function, the one-sided fractional operators, or one-sided maximal operators given by the convolution with a smooth function. We also prove that b ∈ BMO is a necessary condition for the bounded...

We study classes of filters F on N such that weak and strong F -convergence of sequences in l1 coincide. We study also analogue of l1 weak sequential completeness theorem for filter convergence.

Abstract In this paper, we propose two iterative schemes for approximating solutions of split common fixed point problems in multiple linear operators case. The first algorithm implements the Krasnosel’skiĭ–Mann iteration with an inertial effect which weak convergence is established under mild assumptions. With tool nearly contractive mappings, introduce a viscosity-type ensures strong converge...