Abstract
If $P,Q:[0,\infty)\to$ are increasing functions and $T$ is the Calderón operator defined on positive or decreasing functions, then optimal modular inequalities $\int P(Tf)\leq C\int Q(f)$ are proved. If $P=Q$, the condition on $P$ is both necessary and sufficient for the modular inequality. In addition, we establish general interpolation theorems for modular spaces.
Citation
María J. Carro. Hans Heinig. "Modular inequalities for the Calderón operator." Tohoku Math. J. (2) 52 (1) 31 - 46, 2000. https://doi.org/10.2748/tmj/1178224656
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