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- W2009351570 abstract "We work on a general nilpotent Lie group G = G 1 ⊕ G 2 ⊕…⊕ G r , where r ⩾1 and G (k) =⊕ j=k r is the descending central series of G . A composition theorem and an L 2 boundedness theorem for convolution operators f → f ★ A are proved. The composition theorem holds for symbols a = A ∧ satisfying the estimates |D α a(ξ)|⩽C α m (ξ)g(ξ) −α , where m is a weight and g(ξ) α =g 1 (ξ) α 1 …g r (ξ) α r , where g k (ξ)= 1+ ∑ j=k+1 r ||ξ j || 2 1 2 1 2 . The class of weights admissible for the calculus is considerably larger than those of the existing calculi. For the L 2 -boundedness it is sufficient that |D α a(ξ)|⩽C α g(ξ) −α . This goes in the direction of Howe's conjecture and improves the results of Howe and Manchon. It is very likely that our methods could also be used to extend the calculus of Melin to general homogeneous groups." @default.
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- W2009351570 date "2004-01-01" @default.
- W2009351570 modified "2023-09-27" @default.
- W2009351570 title "A symbolic calculus and L2-boundedness on nilpotent Lie groups" @default.
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- W2009351570 doi "https://doi.org/10.1016/s0022-1236(03)00112-5" @default.
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