Classical Fourier Analysis

By Loukas Grafakos. 2010

3,078 citations recorded by the source corpus.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/b0c4f3d96ad476d1e4f377074cd5414973d3cd92

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In Applied Mathematics

1. Dachun Yang
2. Wen Yuan
3. Ciqiang Zhuo
4. Jun Liu
5. Yoshihiro Sawano
6. Yiyu Liang
7. Yuan Zhou
8. Yangyang Zhang

Citations in the corpus

• Fourier Multipliers for Hardy Spaces of Dirichlet Series (2012, neutral): “articular, this implies that we can make kTMf − Tm◦rfkLp(Td) arbitrarily small. In light of (4), to obtain the desired inequality, we infer that it suffices to prove kTMfkLp(Td) ≤ km◦exp(Q −1·)k Mp(T). (5) To verify (5), let us first employ the change of variables θ = ATθ′ to get kTMfk p Lp(Td) = Z Td ”
• A new look at the fractional Poisson problem via the logarithmic Laplacian (2019, neutral): “[21, 26]).”
• Characterization of Lipschitz spaces via commutators of the Hardy–Littlewood maximal function (2016, background): “The following strong and weak-type boundedness of Mα are well-known, see [10] and [7].”
• Sharp bounds for m-linear Hardy and Hilbert Operators (2012, neutral): “0 T (1)(f)(x)g(x) dx ≤ π sin(π/p) ‖f‖Lp(0,∞)‖g‖Lp′ (0,∞), where 1 p + 1 p′ = 1, 1 < p <∞; see for instance [13], [10], and [6].”
• Maximal Operator for Multilinear Singular Integrals with Non-smooth Kernels (2009, background): “This result was proved in [GT3] via the m-linear Cotlar inequality; the latter generalizes the linear Cotlar inequality (see [C], [G], and [St]).”
• Fractional div-curl quantities and applications to nonlocal geometric equations (2017, background): “An integro-differential Triebel–Lizorkin type space The Sobolev space W (R), s ∈ (0, 1), p ∈ (1,∞) is equivalent to the Triebel–Lizorkin spaces F s p,2(R ), see [18, 17, 31].”
• Monotone operator theory for unsteady problems in variable exponent spaces (2012, background): “The operator M : f M f is called Hardy–Littlewood maximal operator or simply maximal operator, see also [28,29] or [30].”