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A Study of the Sequence of Norm of Derivatives (or Primitives) of Functions Depending on Their Beurling Spectrum

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Abstract

In this paper, we characterize the behavior of the sequence of norm of derivatives (or primitives) of functions by their Beurling spectrum in Banach spaces. The Bernstein inequality for Banach spaces is also obtained.

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Acknowledgments

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2011.32. The authors would like to thank the referees for the exact corrections.

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Authors and Affiliations

  1. Institute of Mathematics, Vietnamese Academy of Science and Technology, 18 Hoang Quoc Viet Street, Cau Giay, Hanoi, Vietnam

    Ha Huy Bang

  2. Department of Mathematics, College of Science, Vietnam National University, 334 Nguyen Trai Street, Thanh Xuan, Hanoi, Vietnam

    Vu Nhat Huy

Authors
  1. Ha Huy Bang
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  2. Vu Nhat Huy
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Correspondence to Ha Huy Bang.

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Bang, H.H., Huy, V.N. A Study of the Sequence of Norm of Derivatives (or Primitives) of Functions Depending on Their Beurling Spectrum. Vietnam J. Math. 44, 419–429 (2016). https://doi.org/10.1007/s10013-015-0146-y

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  • DOI: https://doi.org/10.1007/s10013-015-0146-y

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