arXiv:2010.08632 Abstract | arXiv Analytics

arXiv:2010.08632 [math.FA]Abstract References Reviews Resources

Optimality of function spaces for kernel integral operators

Published 2020-10-16Version 1

We explore boundedness properties of kernel integral operators acting on rearrangement-invariant (r.i.) spaces. In particular, for a given r.i. space $X$ we characterize its optimal range partner, that is, the smallest r.i. space $Y$ such that the operator is bounded from $X$ to $Y$. We apply the general results to Lorentz spaces to illustrate their strength.

Comments: 27 pages, submitted to Matematische Nachrichten

Categories: math.FA

Subjects: 47B34, 46E30

Keywords: function spaces, optimality, optimal range partner, boundedness properties, lorentz spaces

Related articles: Most relevant | Search more

arXiv:1211.5947 [math.FA] (Published 2012-11-26)

Interpolation of Ces{à}ro sequence and function spaces

Sergey V. Astashkin, Lech Maligranda

arXiv:1401.5906 [math.FA] (Published 2014-01-23, updated 2014-09-03)

Nonlinear subsets of function spaces and spaceability

César Ruiz, Víctor M. Sánchez

arXiv:1410.6327 [math.FA] (Published 2014-10-23)