Abstract
We prove an analogue of Riesz-Thorin-Stein-Weiss interpolation theorem in the weighted Lebesgue-Morrey setting (a generalization of Campanato– Murthy interpolation theorem to the case of weighed spaces).
Mathematics Subject Classification (2010). Primary 46E30.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Bergh and J. Löfström, Interpolation spaces. An Introduction. Springer, Berlin, 1976.
S. Campanato and M.K.V. Murthy, Una generalizzazione del teorema di Riesz- Thorin. Ann. Scuola Norm. Super. Pisa, Classe di Scienze 3 serie, 3(19) (1965), 87–100.
A. Fiorenza, B. Gupta and P. Jain, The maximal theorem in weighted grand Lebesgue spaces. Studia Math., 188(2) (2008), 123–133.
T. Iwaniec and C. Sbordone, On the integrability of the Jacobian under minimal hypotheses. Arch. Rational Mech. Anal., 119 (1992), 129–143.
A. Meskhi, Maximal functions and singular integrals in Morrey spaces associated with grand Lebesgue spaces. Proc. A. Razmadze Math. Inst., 151 (2009), 139–143.
J. Peetre, On the theory of ℒ p ,⋋ spaces, J. Funct. Anal., 4 (1969), 71–87.
S.G. Samko and S.M. Umarkhadzhiev, On Iwaniec-Sbordone spaces on sets which may have infinite measure. Azerbaijan J. of Mathematics, 1(1) (2011), 67–84.
E.M. Stein and G. Weiss, Interpolation of operators with change of measures. Trans. Amer. Math. Soc., 87 (1958), 159–172.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Additional information
Dedicated with great pleasure to Stefan Samko on the occasion of his 70th birthday
Rights and permissions
Copyright information
© 2013 Springer Basel
About this paper
Cite this paper
Umarkhadzhiev, S.M. (2013). Riesz-Thorin-Stein-Weiss Interpolation Theorem in a Lebesgue-Morrey Setting. In: Almeida, A., Castro, L., Speck, FO. (eds) Advances in Harmonic Analysis and Operator Theory. Operator Theory: Advances and Applications, vol 229. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0516-2_22
Download citation
DOI: https://doi.org/10.1007/978-3-0348-0516-2_22
Published:
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0515-5
Online ISBN: 978-3-0348-0516-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)