Abstract:
We get new sufficient conditions for Fourier multipliers in
Hardy spaces $H_p(\mathbb R^n)$, $0<p\le 1$, and $L_p(\mathbb R^n)$,
$1\le p\le\infty$. Being of a multiplicative character, these conditions
are stated in terms of the joint behaviour of ‘norms’ of functions
in $L_q(\mathbb R^n)$ and Besov spaces $B_{r,\infty}^s(\mathbb R^n)$.
Keywords:
Fourier multipliers, Hardy spaces, Besov spaces, Wiener algebra.
This publication is cited in the following 10 articles:
Kolomoitsev Yu., “P Approximation By Quasi-Interpolation Operators and Smolyak'S Algorithm”, J. Complex., 69 (2022), 101601
Fang J., Li H., Zhao J., “Multilinear and Multiparameter Spectral Multipliers on Homogeneous Besov and Triebel-Lizorkin Spaces on Lie Groups of Polynomial Growth”, J. Geom. Anal., 32:3 (2022), 100
Yu. Kolomoitsev, M. Skopina, “Uniform approximation by multivariate quasi-projection operators”, Anal.Math.Phys., 12:2 (2022)
Kolomoitsev Yu., Prestin J., “Approximation Properties of Periodic Multivariate Quasi-Interpolation Operators”, J. Approx. Theory, 270 (2021), 105631
Kolomoitsev Yu., Skopina M., “Approximation By Multivariate Quasi-Projection Operators and Fourier Multipliers”, Appl. Math. Comput., 400 (2021), 125955
Kolomoitsev Yu., Skopina M., “Approximation By Sampling-Type Operators in Lp-Spaces”, Math. Meth. Appl. Sci., 43:16 (2020), 9358–9374
Fang J., Zhao J., “H-P Boundedness of Multilinear Spectral Multipliers on Stratified Groups”, J. Geom. Anal., 30:1 (2020), 197–222
Yurii Kolomoitsev, Tetiana Lomako, Applied and Numerical Harmonic Analysis, Topics in Classical and Modern Analysis, 2019, 183
Yu. Kolomoitsev, E. Liflyand, “On weighted conditions for the absolute convergence of Fourier integrals”, J. Math. Anal. Appl., 456:1 (2017), 163–176
S. Krol, “Fourier multipliers on the real Hardy spaces”, Archiv der Mathematik, 106:5 (2016), 457–470
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