The question of the boundedness of integral transforms defined on spaces of homogeneous type (SHT) arises naturally when studying boundary-value problems for partial differential equations with variable coefficients. For example, when the underlying domain is strongly pseudo-convex, one is led to use the concept of the Heisenberg group (and more general structures) as a model for the boundary of the domain in the theory of functions of several complex variables. Such problems indicate a strong need for structures more general than spaces of functions on Euclidean space. The space domain might, for instance, be most conveniently endowed with a quasi-metric induced by a differential operator or tailored to suit the kernel of a given integral operator (see , Chapters I, XII and XIII).
KeywordsWeight Function Integral Operator Heisenberg Group Singular Integral Type Inequality
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