Open AccessOn boundedness of operators of weak type $(\varphi_0, \psi_0, \varphi_1, \psi_1)$ in Lorentz spaces in limit cases
Author(s) -
B.I. Peleshenko
Publication year - 2021
Publication title -
researches in mathematics
Language(s) - English
Resource type - Journals
eISSN - 2664-5009
pISSN - 2664-4991
DOI - 10.15421/240716
Subject(s) - lorentz transformation , limit (mathematics) , infinity , lorentz space , mathematics , type (biology) , space (punctuation) , zero (linguistics) , lambda , mathematical physics , combinatorics , pure mathematics , mathematical analysis , physics , quantum mechanics , philosophy , ecology , linguistics , biology
We prove theorems on boundedness of operators of weak type $(\varphi_0, \psi_0, \varphi_1, \psi_1)$ from Lorentz space $\Lambda_{\varphi,a}(\mathbb{R}^n)$ to $\Lambda_{\varphi,b}(\mathbb{R}^n)$ in “limit” cases, when one of functions $\varphi(t) / \varphi_0(t)$, $\varphi(t) / \varphi_1(t)$ slowly changes at zero and at infinity.