Hostname: page-component-669899f699-2mbcq Total loading time: 0 Render date: 2025-05-02T22:34:12.896Z Has data issue: false hasContentIssue false
  • English
  • Français

Remarks on countable subadditivity

Part of: Harmonic analysis in one variable General theory of linear operators Harmonic analysis in several variables

Published online by Cambridge University Press:  23 August 2023

Loukas Grafakos Open the ORCID record for Loukas Grafakos [Opens in a new window]  and
Monica Vişan
Loukas Grafakos
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211, USA ([email protected])
Monica Vişan
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA 90095, USA ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

We discuss how countable subadditivity of operators can be derived from subadditivity under mild forms of continuity, and provide examples manifesting such circumstances.

Keywords

Interpolationadditivitysubadditivity

MSC classification

Primary: 47A30: Norms (inequalities, more than one norm, etc.)
Secondary: 47A63: Operator inequalities 42A99: None of the above, but in this section 42B35: Function spaces arising in harmonic analysis
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 154 , Issue 5 , October 2024 , pp. 1504 - 1517
Check for updates
Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Aoki, T.. Locally bounded spaces. Proc. Imp. Acad. Tokyo 18 (1942), 585–634.Google Scholar
Calderón, A.-P.. Intermediate spaces and interpolation. (Studia Math. Ser. Specjalna) Zeszyt 1 (1963), 31–34.Google Scholar
Calderón, A.-P.. Intermediate spaces and interpolation, the complex method. Studia Math. 24 (1964), 113–190.10.4064/sm-24-2-113-190CrossRefGoogle Scholar
Carro, M. J. and Martín, J.. Extrapolation theory for the real interpolation method. Collect. Math. 53 (2002), 165–186.Google Scholar
Grafakos, L., Classical Fourier Analysis, 3rd Ed. Graduate Texts in Math. Vol. 249 (Springer, NY, 2014).CrossRefGoogle Scholar
Grafakos, L. and Kalton, N. J.. The Marcinkiewicz multiplier condition for bilinear operators. Studia Math. 146 (2001), 115–156.10.4064/sm146-2-2CrossRefGoogle Scholar
Hunt, R. A.. An extension of the Marcinkiewicz interpolation theorem to Lorentz spaces. Bull. Amer. Math. Soc. 70 (1964), 803–807.10.1090/S0002-9904-1964-11242-8CrossRefGoogle Scholar
Hunt, R. A.. On L(p,q) spaces. Enseignement Math 12 (1966), 249–276.Google Scholar
Kalton, N. J., Peck, N. T. and Roberts, J. W., An $F$-space Sampler, London Mathematical Society Lecture Notes Series, Vol. 89 (Cambridge University Press, Cambridge, 1984).CrossRefGoogle Scholar
Krein, S. G. and Semenov, E. M.. A scale of spaces. Dokl. Akad. Nauk SSSR 138 (1961), 763–766.Google Scholar
Lions, J.-L. and Peetre, J.. Sur une classe d'espaces d’ interpolation. Inst. Hautes Études Sci., Publ. Math. No. 19 (1964), 5–68.10.1007/BF02684796CrossRefGoogle Scholar
Peetre, J.. Nouvelles propriétés d'espaces d’ interpolation. C. R. Acad. Sci. Paris 256 (1963), 1424–1426.Google Scholar
Rolewicz, S., Metric Linear Spaces, 2nd Ed., Mathematics and its Applications (East European Series), Vol. 20. D. Reidel Publishing Co., Dordrecht; PWN–Polish Scientific Publishers, Warsaw, 1985).Google Scholar
Stein, E. M., Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, Vol. 43, Monographs in Harmonic Analysis, III. (Princeton University Press, Princeton, NJ, 1993).10.1515/9781400883929CrossRefGoogle Scholar
Stein, E. M. and Weiss, G.. Interpolation of operators with change of measures. Trans. Am. Math. Soc. 87 (1958), 159–172.10.1090/S0002-9947-1958-0092943-6CrossRefGoogle Scholar
Stein, E. M. and Weiss, G.. An extension of a theorem of Marcinkiewicz and some of its applications. J. Math. Mech. 8 (1959), 263–284.Google Scholar
Stein, E. M. and Weiss, G., Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, Vol. 32 (Princeton University Press, Princeton, N.J., 1971).Google Scholar
Yano, S.. Notes on Fourier analysis, XXIX, An extrapolation theorem. J. Math. Soc. Jpn 3 (1951), 296–305.CrossRefGoogle Scholar