Embeddings of some classical Banach spaces into modulation spaces

By Kasso Okoudjou. 2004

81 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/e948b43ac2cb4356853fdadf09ca5a65d54b4737

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In Applied Mathematics

In Computer Vision and Pattern Recognition

Citations in the corpus

WIENER RANDOMIZATION ON UNBOUNDED DOMAINS AND AN APPLICATION TO ALMOST SURE WELL-POSEDNESS OF NLS (2014, background): “There are several known embeddings between the Besov, Sobolev, and modulation spaces; see, for example, Okoudjou [40], Toft [51], Sugimoto-Tomita [48], and Kobayashi-Sugimoto [35].”
Approximation of the Fourier Transform and the Dual Gabor Window (2005, background): “For just convergence in Lp, 1 ≤ p ≤ ∞, the coefficients can be omitted for Ln. Note that convergence in Lp is considered here for f ∈ S0 and not for general Lp-functions.”
The Segal Algebra ${\bf S}_0({\Bbb R}^d)$ and Norm Summability of Fourier Series and Fourier Transforms (2006, background): “Proof. (i) was proved in Girardi and Weis [11] and (ii) in Okoudjou [ 20 ].”
Frequency-uniform decomposition method for the generalized BO, KdV and NLS equations (2007, methodology): “1 and our technique is the frequency-uniform decomposition method applied in [11, 40], which is different from those in [28,34].”
Modulation Spaces on Locally Compact Abelian Groups (2003, background): “Okoudjou ([102]) and Toft [111, 112], but one should also mention [85] and [93] in this context.”
Highly sparse representations from dictionaries are unique and independent of the sparseness measure (2007, unknown): “dilation and modulation in [16], as well as embeddings of Besov spaces into modulation spaces in [37]).”
On the Probabilistic Cauchy Theory of the Cubic Nonlinear Schrödinger Equation on Rd, d≥3 (2014, background): “ous) Besov spaces Bp,q s via the norm kukBs p,q(Rd) = 2jskϕ j(D)ukLp(Rd) ℓq j(Z≥0) . (1.8) There are several known embeddings between Besov, Sobolev, and modulation spaces. See, for example, Okoudjou [47], Toft [59], Sugimoto-Tomita [55], and Kobayashi-Sugimoto [40]. Now, given a function φon Rd, we”
Summability of Multi-Dimensional Trigonometric Fourier Series (2012, unknown): “[67] K. A. Okoudjou.”
Finite Discrete Gabor Analysis (2007, background): “There exists many useful conditions for membership of S0(R), see [37, 41, 76].”
Unimodular Fourier multipliers for modulation spaces (2006, background): “Since α ≤ 1, all partial derivatives of σosc are bounded, and this fact implies that σosc ∈ C d+1 (R d ) ⊂ M ∞,1 (R d ). For this embedding, see, e.g., [13, Thm. 14.5.3] or [ 21 ].”
MODULATION SPACES AND A CLASS OF BOUNDED MULTILINEAR PSEUDODIFFERENTIAL OPERATORS (2005, methodology): “We conclude this section by listing a few embeddings proved in [23] between Lebesgue or Besov spaces and modulation spaces.”
Local well‐posedness of nonlinear dispersive equations on modulation spaces (2007, background): “There exist several embedding results between Lebesgue, Sobolev, or Besov spaces and modulation spaces, see for example [ 11 ], [13]; also [1], [2].”
Ultradistributions and Time-Frequency Analysis (2006, background): “Inclusion relations between modulation spaces and other spaces of functions or distributions (L, Besov and Sobolev spaces) are given in [13], [19], [28], [46].”
Micro-local analysis in Fourier Lebesgue and modulation spaces: part II (2008, background): “ construction of these spaces, it turns out that modulation spaces and Besov spaces in some sense are rather similar, and sharp embeddings between these spaces can be found in [1,28,32,33]. (See also [9,21] for other embeddings.) Parallel to this development, modulation spaces have been incorporated”
Micro-Local Analysis with Fourier Lebesgue Spaces. Part I (2011, unknown): “(See also [9] [21] for other embeddings.)”