The necessary and sufficient conditions are found for the weight function v, which provide the boundedness and compactness of the Riemann–Liouville operator Rα from Lp to L q v . The criteria are also established for the weight function w, which guarantee the boundedness and compactness of the Weyl operator Wα from L p w to Lq . In this paper, the necessary and sufficient conditions are found f...

In this work, we study the existence of periodic solutions for partial neutral functional differential equation. We assume that the linear part is not necessarily densely defined and satisfies the Hille-Yosida condition. In the nonhomogeneous linear case, we prove that the existence of a bounded solution on R+ implies the existence of a periodic solution. In nonlinear case, we use the concept o...

We characterize KMS thermal equilibrium states, at Hawking temperature β, for the Killing evolution associated with a class of stationary quantum black holes in terms of a boundedness property, namely the localized state vectors should have energy density levels increasing β-subexponentially; a property which is similar in the form and weaker in the spirit than the modular compactness-nuclearit...

We consider generalized Morrey spaces Mp,ω R with a general function ω x, r defining the Morrey-type norm. We find the conditions on the pair ω1, ω2 which ensures the boundedness of the maximal operator and Calderón-Zygmund singular integral operators from one generalized Morrey space Mp,ω1 R to another Mp,ω2 R , 1 < p < ∞, and from the space M1,ω1 R to the weak space WM1,ω2 R . We also prove a...

We address the strategy problem for parity games with partial information and observable colors, played on finite graphs of bounded graph complexity. We consider several measures for the complexity of graphs and analyze in which cases, bounding the measure decreases the complexity of the strategy problem on the corresponding classes of graphs. We prove or disprove that the usual powerset constr...

Clique-width is an important graph parameter due to its algorithmic and structural properties. A graph class is hereditary if it can be characterized by a (not necessarily finite) set H of forbidden induced subgraphs. We initiate a systematic study into the boundedness of clique-width of hereditary graph classes closed under complementation. First, we extend the known classification for the |H|...

The aim of this article is to study the $L^p$-boundedness pseudo-differential operators on a homogeneous tree $ \mathfrak X $. For $p\in (1,2)$, we establish connection between $L^{p}$-boundedness \mathfr

In this paper we examine how it is possible to control Petri net behavior with the help of time constraints. Controlling here means to force a process to behave in a desirable way by ascribing priorities to transitions and hence transforming a classic Petri net into a Priority Petri net. Liveness and boundedness are crucial properties in many application areas, e.g. workflow modeling and bioinf...

In this paper, the stability of translation-invariant spaces of distributions over locally compact groups is stated as boundedness of synthesis and projection operators. At first, a characterization of the stability of spline-type spaces is given, in the standard sense of the stability for shift-invariant spaces, that is, linear independence characterizes lower boundedness of the synthesis oper...