In this paper we use a unified way studying the decay estimate for a class of dispersive semigroup given by e itφ(√ −∆) , where φ : R + → R is smooth away from the origin. Especially, the decay estimates for the solutions of the Klein-Gordon equation and the beam equation are simplified and slightly improved.
Let NAK be the Iwasawa decomposition of group SU(n + 1, 1). The Iwasawa subgroup P = NA can be identified with the generalized upper half–plane U n+1 and has a natural representation U on the L 2 –space of the Heisenberg group L 2 (H n). We decompose L 2 (H n) into the direct sum of the irreducible invariant closed subspaces under U. The restrictions of U… (More)
For 2 (?1; 1), let Q (R n) be the space of all measurable functions with supp`(I)] 2?n Z I Z I jf(x) ? f(y)j 2 jx ? yj n+2 dx dy < 1; where the supremum is taken over all cubes I with the edge length`(I) and the edges parellel to the coordinate axes in R n. If 2 (?1; 0), then Q (R n) = BMO(R n), and if 2 1; 1), then Q (R n) = fconstantsg. In the present… (More)
The parametrization for one kind of multifilter banks generating balanced multiwavelets is presented in this paper, in which two lowpass filters are flipping filters, and two highpass filters have linear phase. Based on these parametric expressions, some balanced multiwavelets and analysis-ready multiwavelets are constructed, which are symmetric, or… (More)
We prove that the KP-I initial-value problem ∂ t u + ∂