Modulation spaces Mp,q for 0

By Masaharu Kobayashi. 2006

62 citations recorded by the source corpus.

The purpose of this paper is to construct modulation spaces Mp,q(Rd) for general 0<p, q≦∞, which coincide with the usual modulation spaces when 1≦p,q≦∞, and study their basic properties including their completeness. Given any g∈S(Rd) such that supp ĝ⊂ {ξ∣|ξ|≦1} and ∑k∈Zdĝ(ξ-αk)≡1, our modulation space consists of all tempered distributions f such that the (quasi)-norm ‖f‖M[g]p,q:≔(∫Rd(∫Rd|f*(Mωg)(x)|pdx)qpdω)1q is finite.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ee49ddca4e8d0333c3e77a65a555f3267615724b

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In Applied Mathematics

In Statistics and Probability

Citations in the corpus

Decompositions of Besov–Morrey spaces and Triebel–Lizorkin–Morrey spaces (2007, unknown): “For example the modulation space M p,q with 0 < p, q ≤ ∞ was considered recently in [5].”
Frequency-uniform decomposition method for the generalized BO, KdV and NLS equations (2007, background): “The authors are also indebted to the referee for his valuable comments and pointing out the reference [23].”
Local well‐posedness of nonlinear dispersive equations on modulation spaces (2007, methodology): “The definition above can be appropriately extended to exponents 0 < p, q ∞ as in the works of Kobayashi [9, 10].”
Remarks on Fourier multipliers and applications to the Wave equation (2008, background): “volving diﬀerent kinds of weight functions, both in the time and the frequency variables we refer to [7]. 3 The Deﬁnition 1 has been accordingly extended to the quasi-Banach case 0 < p,q < 1 in [8, 9]. Here the window function g is to be restricted to the class ( g ∈ S(Rd) : suppˆg ⊂ {ξ : |ξ| ”