Some extensions of the Marcinkiewicz interpolation theorem in terms of modular inequalities

María J. CARRO; Ludmila NIKOLOVA

doi:10.2969/jmsj/1191419122

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

Some extensions of the Marcinkiewicz interpolation theorem in terms of modular inequalities

María J. CARRO, Ludmila NIKOLOVA

著者情報

キーワード: Boundedness of operators, Interpolation, Modular Inequalities

ジャーナルフリー

2003 年 55 巻 2 号 p. 385-394

DOI https://doi.org/10.2969/jmsj/1191419122

詳細

抄録

Given a quasi-subaditive operator T:L₀(μ)→ L₀(v), we want to study mapping properties of interpolation type for which the following modular inequality holds \[∈t_{\mathscr{N}}P(|Tf(x)|)dv(x)≤∈t_{\mathscr{M}}Q(|f(x)|)dμ(x) \] where P and Q are modular functions. These results generalize the classical Marcinkiewicz interpolation theorem.