Tohoku Mathematical Journal

Modular inequalities for the Calderón operator

María J. Carro and Hans Heinig

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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.

Article information

Source
Tohoku Math. J. (2), Volume 52, Number 1 (2000), 31-46.

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178224656

Digital Object Identifier
doi:10.2748/tmj/1178224656

Mathematical Reviews number (MathSciNet)
MR1740541

Zentralblatt MATH identifier
1057.46060

Subjects
Primary: 46M35: Abstract interpolation of topological vector spaces [See also 46B70]
Secondary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Citation

Carro, María J.; Heinig, Hans. Modular inequalities for the Calderón operator. Tohoku Math. J. (2) 52 (2000), no. 1, 31--46. doi:10.2748/tmj/1178224656. https://projecteuclid.org/euclid.tmj/1178224656


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