Edmunds, D. E.; Kokilashvili, V.; Meskhi, A. Weight inequalities for singular integrals defined on spaces of homogeneous and nonhomogeneous type. (English) Zbl 1002.42009 Georgian Math. J. 8, No. 1, 33-59 (2001). 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. By a space of nonhomogeneous type the authors mean a measure space with a quasimetric; however, the doubling condition is not assumed and may fail. In the nonhomogeneous case, the results of the authors are also new even in Lebesgue spaces. Reviewer: Yang Dachun (Beijing) Cited in 1 Document MSC: 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.) 43A85 Harmonic analysis on homogeneous spaces 42B25 Maximal functions, Littlewood-Paley theory 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) Keywords:singular integral; maximal function; Hardy-type operator; space of homogeneous type; space of nonhomogeneous type; Lorentz space PDFBibTeX XMLCite \textit{D. E. Edmunds} et al., Georgian Math. J. 8, No. 1, 33--59 (2001; Zbl 1002.42009) Full Text: EuDML EMIS