• Media type: E-Article
  • Title: Equivalent characterizations of martingale Hardy–Lorentz spaces with variable exponents
  • Contributor: Weisz, Ferenc
  • Published: Springer Science and Business Media LLC, 2024
  • Published in: Revista Matemática Complutense, 37 (2024) 3, Seite 783-800
  • Language: English
  • DOI: 10.1007/s13163-023-00472-3
  • ISSN: 1988-2807; 1139-1138
  • Origination:
  • Footnote:
  • Description: AbstractWe prove that under the log-Hölder continuity condition of the variable exponent $$p(\cdot )$$ p ( · ) , a new type of maximal operators, $$U_{\gamma ,s}$$ U γ , s is bounded from the variable martingale Hardy–Lorentz space $$H_{p(\cdot ),q}$$ H p ( · ) , q to $$L_{p(\cdot ),q}$$ L p ( · ) , q , whenever $$0<p_-\le p_+ <\infty $$ 0 < p - ≤ p + < ∞ , $$0<q \le \infty $$ 0 < q ≤ ∞ , $$0<\gamma ,s<\infty $$ 0 < γ , s < ∞ and $$1/p_- - 1/p_+ < \gamma +s$$ 1 / p - - 1 / p + < γ + s . Moreover, the operator $$U_{\gamma ,s}$$ U γ , s generates equivalent quasi-norms on the Hardy–Lorentz spaces $$H_{p(\cdot ),q}$$ H p ( · ) , q .