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

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

Integral Transforms and Special Functions, cilt.27, sa.4, ss.318-330, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 27 Sayı: 4
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1080/10652469.2015.1121483
  • Dergi Adı: Integral Transforms and Special Functions
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.318-330
  • Anahtar Kelimeler: 42B20, 42B35, 47G10, Local Morrey-Lorentz spaces, Hilbert transform, Hardy operator, modified Hilbert transform, HARDY
  • Ankara Üniversitesi Adresli: Evet

Özet

© 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.