Fractional integral operators on α-modulation spaces

Abstract

Key words Fractional integral operators, α-modulation space, Besov space, sharp conditions MSC (2010) 42B15, 42B35In this paper, we give the sufficient and necessary conditions for the boundedness of fractional integral operators on the α-modulation spaces. The main theorem substantially extends and improves some known results.

Orthogonality of the bilinear Fourier multiplier in the modulation spaces

“…利用命题 1.4 的思想, 我们可以进一步刻画一些具体的 Fourier 乘子在模空间中的有界性. 例如, 关于分数次积分算子的有界性可以参见文献 [23][24][25], 关于幺模乘子在模空间中的有界性可以参见文 献 [14,15].…”

Unimodular multipliers on $$\alpha$$-modulation spaces: a revisit with new method

“…Among numerous references on -modulation spaces, one can see [21,27] for elementary properties of -modulation spaces, see [20] for the full characterization of embedding between -modulation spaces, see [30,33,35] for the research of boundedness of fractional integrals and see [4][5][6][7] for the study of pseudodifferential operators and nonlinear appoximation. We also point out that the boundedness of unimodular multipliers on -modulation spaces has been studied in [31,32], in which if we take = 0 , the result is in accordance to that in [22].…”

On homogeneous decomposition spaces and associated decompositions of distribution spaces

“…[7,8,20,26,37] and references therein. This is in part motivated by applications to signal and image processing of generalized wavelet systems such as -modulation frames, see [6,15,16,29,38], and Shearlet type systems, see [7,[24][25][26]. The second generation curvelet systems are generally based on modified decompositions of the frequency domain as compared to the classical dyadic decompositions.…”