The boundedness of Bessel–Riesz operators defined on Lebesgue spaces and Morrey in measure metric is discussed this research study. maximal operator traditional dyadic decomposition are used to study the Bessel-Riesz operators. We investigate interaction between kernel space parameters get results see how affects kernel-bound

For a symmetric kernel k : X × X → R ∪ {+∞} on a locally compact metric space X, we investigate the asymptotic behavior of greedy k-energy points {ai}1 for a compact subset A ⊂ X that are defined inductively by selecting a1 ∈ A arbitrarily and an+1 so that ∑n i=1 k(an+1, ai) = infx∈A ∑n i=1 k(x, ai). We give sufficient conditions under which these points (also known as Leja points) are asymptot...

We consider a functional on the Wiener space which is smooth and not degenerated in Malliavin sense and we give a criterion for the strict positivity of the density, that we can use to state lower bounds as well. The results are based on the representation of the density in terms of the Riesz transform introduced in Malliavin and Thalmaier bib:[M.T] [16] and on the estimates of the Riesz transf...

In this paper, we consider linear space-time fractional reactiondiffusion equation with composite fractional derivative as time derivative and Riesz-Feller fractional derivative with skewness zero as space derivative. We apply Laplace and Fourier transforms to obtain its solution.

This is a set of lecture notes which present an economical development of measure theory and integration in locally compact Hausdorff spaces. We have tried to illuminate the more difficult parts of the subject. The Riesz-Markov theorem is established in a form convenient for applications in modern analysis, including Haar measure on locally compact groups or weights on C∗-algebras...though appl...

*Correspondence: [email protected] 3Faculty of Science and Technology, Tapee College, Surathani, 84000, Thailand Full list of author information is available at the end of the article Abstract In this paper, we obtain new Riesz representations of continuous linear maps associated with certain boundary value problems in the set of all closed bounded convex non-empty subsets of any Banach sp...

We examine condition numbers, preconditioners, and iterative methods for finite element discretizations of coercive PDEs in the context of the fundamental solvability result, the Lax-Milgram Lemma. Working in this Hilbert space context is justified because finite element operators are restrictions of infinite-dimensional Hilbert space operators to finite-dimensional subspaces. Moreover, useful ...