N ov 2 00 4 L p - estimates for Riesz transforms on forms in the Poincaré space
نویسنده
چکیده
Using hyperbolic form convolution with doubly isometry-invariant kernels, the explicit expression of the inverse of the de Rham laplacian ∆ acting on m-forms in the Poincaré space H is found. Also, by means of some estimates for hyperbolic singular integrals, L-estimates for the Riesz transforms ∇i∆−1, i ≤ 2, in a range of p depending on m,n are obtained. Finally, using these, it is shown that ∆ defines topological isomorphisms in a scale of Sobolev spaces H m,p(H ) in case m 6= n±1 2 , n 2 . Mathematics Subject Classification(2000): 53C21, 58J05, 58J50, 58J70
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