Hardy's inequalities for Hermite and Laguerre expansions revisited

• Kanjin Yuichi

  Mathematics Section, Division of Innovative Technology and Science, Graduate School of Natural Science and Technology, Kanazawa University

Abstract

We show that Hardy's inequalities for Laguerre expansions hold on the space L¹(0,∞) when the Laguerre parameters α are positive, and we prove that although the inequality holds on the real Hardy space H¹(0,∞) if α = 0, it does not hold on L¹(0,∞). Further, Hardy's inequality for Hermite expansion is established on L¹(0,∞).

Journal

• Journal of the Mathematical Society of Japan

  Journal of the Mathematical Society of Japan 63 (3), 753-767, 2011

  The Mathematical Society of Japan

Keywords

• Hardy's inequality
• Hermite expansion
• Laguerre expansion

Details

• CRID: 1390001205115861632
• NII Article ID: 10029321824
• NII Book ID: AA0070177X
• DOI: 10.2969/jmsj/06330753
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• NDL BIB ID: 11170132
• Web Site: http://hdl.handle.net/2297/29460
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I11170132
• Text Lang: en
• Data Source:
  • JaLC
  • IRDB
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed