Singular integrals on bounded symmetric domains in [formula omitted

Abstract

Let D be a bounded symmetric domain in the complex vector space CT (N > 1) with 0 E D. The domain D is circular and star-shaped with respect to 0. The group G of holomorphic automorphisms of D is transitive on D and extends continuously to the topological boundary of D. The domain D has a Bergman-Silov boundary b, which is a compact real-analytic submanifold of CN. Also b is circular and invariant under G and the isotropy group G, = (g E G ] g(0) = 0) is transitive on b. The boundary b has a unique normalized Go-invariant measure p given by c$, = l/V&,, V the Euclidean volume of 6, and ds, the Euclidean volume element at t E b. Let H(D) be the set of holomorphic functions on D. The Hardy H9 = H9(D) space (4 > 0) is the set of functions in H(D) with finite not-m llfll, = su~~.,,,(l/~1',lf(rt)l~ ds,)': bf 0~)) and llfll. = SUPO 1, H9 is a Banach space and for 0 < q < 1 a complete linear Hausdorff space [2]. A function f in H9(D) has a Fourier series expansion