A weighted weak-type inequality for the one-sided maximal operators

  • J. Wang School of Mathematics and Statistics, Henan University of Science and Technology, China
  • Y. Ren School of Mathematics and Statistics, Yancheng Teachers University, China
  • E. Zhang School of Mathematics and Statistics, Henan University of Science and Technology, China
Keywords: weight, weak type inequality, one-sided maximal operator, Orlicz class

Abstract

UDC 517.5

We obtain some necessary and sufficient conditions for a weighted weak-type inequality of the form $$\int\limits_{\{M_g^{+}(f)>\lambda\}}\widetilde{\varphi}\left(\frac{\lambda}{\omega_{3}(x)\omega_{4}(x)}\right)\omega_{4}(x)\,dx\leq C_1\int\limits_{-\infty}^{+\infty}\widetilde{\varphi}\left(C_{1}\frac{|f(x)|}{\omega_{1}(x)\omega_{2}(x)}\right)\omega_{2}(x)\,dx$$ to be true, which generalize some known results.

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Published
24.05.2023
How to Cite
WangJ., RenY., and ZhangE. “A Weighted Weak-Type Inequality for the One-Sided Maximal Operators”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 5, May 2023, pp. 712- 720, doi:10.37863/umzh.v75i5.7062.
Section
Short communications