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Two-weight inequalities for singular integrals defined on homogeneous groups. (English) Zbl 0983.43501
Kokilashvili, V. (ed.), Collected papers on the weight theory. Tbilisi: Publishing House GCI, Proc. A. Razmadze Math. Inst. 112, 57-90 (1997).
Summary: Sufficient conditions for pairs of weights ensuring the validity of two-weight strong $$(p,p)$$ and weak (1,1) type inequalities for singular integrals defined on homogeneous groups are found. In some cases these conditions are as well necessary for the corresponding inequalities to be fulfilled. Sufficient conditions for which two-weight inequalities are valid of a strong type $$(p,q)$$ for $$1<q< p<\infty$$ and of a weak type $$(p,1)$$ for $$p>1$$ for singular integrals are also found. In most cases examples for pairs of weights are given.
For the entire collection see [Zbl 0868.00019].

##### MSC:
 43A80 Analysis on other specific Lie groups 42B25 Maximal functions, Littlewood-Paley theory 46E40 Spaces of vector- and operator-valued functions 47G10 Integral operators
##### Keywords:
pairs of weights; singular integrals; homogeneous groups