Abstract
Optimal sufficient conditions are found in weighted Lorentz spaces for weight functions which provide the boundedness of the Calderón–Zygmund singular integral operator defined on spaces of homogeneous and nonhomogeneous type.
Editor-in-Chief: Kiguradze, Ivan / Shervashidze, T.
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Weight Inequalities for Singular Integrals Defined on Spaces of Homogeneous and Nonhomogeneous Type
1Centre for Mathematical Analysis and its Applications, University of Sussex, Brighton BN1 9QH, Sussex, United Kingdom. E-mail: D.E.Edmunds@sussex.ac.uk
2A. Razmadze Mathematical Institute, Georgian Academy of Sciences, 1, M. Aleksidze St., Tbilisi 380093, Georgia. E-mail: kokil@rmi.acnet.ge
3A. Razmadze Mathematical Institute, Georgian Academy of Sciences, 1, M. Aleksidze St., Tbilisi 380093, Georgia. E-mail: meskhi@rmi.acnet.ge
Citation Information: Georgian Mathematical Journal. Volume 8, Issue 1, Pages 33–59, ISSN (Online) 1072-9176, ISSN (Print) 1072-947X, DOI: 10.1515/GMJ.2001.33, February 2010
Publication History:
- Received:
- 2000-08-23
- Published Online:
- 2010-02-23
Key words and phrases:: Singular Integral; maximal function; Hardy-type operator; space of homogeneous type; space of nonhomogeneous type; Lorentz space
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