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Modulation space estimates for the fractional integral operators

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Abstract

We obtain the boundedness for the fractional integral operators from the modulation Hardy space µ p,q to the modulation Hardy space µ r,q for all 0 < p < ∞. The result is an extension of the known result for the case 1 < p < ∞ and it contains a larger range of r than those in the classical result of the L p → L r boundedness in the Lebesgue spaces. We also obtain some estimates on the modulation spaces for the bilinear fractional operators.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Yong Zhong & JieCheng Chen

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    JieCheng Chen

Authors
  1. Yong Zhong
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  2. JieCheng Chen
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Correspondence to JieCheng Chen.

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Zhong, Y., Chen, J. Modulation space estimates for the fractional integral operators. Sci. China Math. 54, 1479–1489 (2011). https://doi.org/10.1007/s11425-011-4215-8

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  • DOI: https://doi.org/10.1007/s11425-011-4215-8

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