The boundedness of Hilbert transform in the local Morrey–Lorentz spaces

Aykol C., Guliyev V., Kucukaslan A., ŞERBETÇİ A.

Integral Transforms and Special Functions, vol.27, no.4, pp.318-330, 2016 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 4
  • Publication Date: 2016
  • Doi Number: 10.1080/10652469.2015.1121483
  • Journal Name: Integral Transforms and Special Functions
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.318-330
  • Keywords: Hardy operator, Hilbert transform, Local Morrey–Lorentz spaces, modified Hilbert transform
  • Ankara Yıldırım Beyazıt University Affiliated: No

Abstract

© 2016 Taylor & Francis.In this paper, we investigate the boundedness of the Hilbert transform H in the local Morrey–Lorentz spaces (Formula presented.) , (Formula presented.) , (Formula presented.). We prove that the operator H is bounded in (Formula presented.) under the condition (Formula presented.) , (Formula presented.). In the limiting case (Formula presented.) , (Formula presented.) , we prove that the operator H is bounded from the space (Formula presented.) to the weak local Morrey–Lorentz space (Formula presented.). Also we show that for the limiting case (Formula presented.) , (Formula presented.) , the modified Hilbert transform (Formula presented.) is bounded from the space (Formula presented.) to the bounded mean oscillation space.