𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the boundedness of some potential-type operators with oscillating kernels

✍ Scribed by Denis N. Karasev; Vladimir A. Nogin

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
282 KB
Volume
278
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We consider a class of multidimensional potential‐type operators with kernels that have singularities at the origin and on the unit sphere and that are oscillating at infinity. We describe some convex sets in the (1/p, 1/q)‐plane for which these operators are bounded from L~p~ into L~q~ and indicate domains where they are not bounded. We also reveal some effects which show that oscillation and singularities of the kernels may strongly influence on the picture of boundedness of the operators under consideration. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 SIMILAR VOLUMES

On the Iterates of Some Bernstein-Type O
On the Iterates of Some Bernstein-Type Operators
✍ José A Adell; F Germán Badı́a; Jesús de la Cal 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 184 KB

In this paper, we establish two basic functional-type identities between the iterates of the Bleimann᎐Butzer᎐Hahn operator and those of the Bernstein Ž . operator, on the one hand, and the iterates of the modified Meyer᎐Konig and Zeller operator and those of the Baskakov operator, on the other. Thes

On the Schur Test forL2-Boundedness of P
On the Schur Test forL2-Boundedness of Positive Integral Operators with a Wiener–Hopf Example
✍ J.F Toland; D Williams 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 397 KB

The Schur sufficiency condition for boundedness of any integral operator with non-negative kernel between L 2 -spaces is deduced from an observation, Proposition 1.2, about the central role played by L 2 -spaces in the general theory of these operators. Suppose (0, M, +) is a measure space and that

On the spectra of some integral operator
On the spectra of some integral operators related to the potential theory in the plane
✍ Oleg F. Gerus; Vladimir N. Kutrunov; Michael Shapiro 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 124 KB 👁 1 views

## Communicated by W. Sprößig We study point spectra of the two integral operators that are generated by the boundary values of the simple-layer potential and of the integral tightly related to the double-layer potential; the operators act on the Hölder space H l (C), l ∈ (0, 1), and on the Lebesg