Conjugate functions on spaces of parabolic Bloch type

• Hishikawa Yôsuke

  Department of General Education, Gifu National College of Technology

• Nishio Masaharu

  Department of Mathematics, Osaka City University

• Yamada Masahiro

  Department of Mathematics, Faculty of Education, Gifu University

抄録

Let H be the upper half-space of the (n+1)-dimensional Euclidean space. Let 0 < α ≤ 1 and m(α) = min {1, 1/(2α)}. For σ > −m(α), the α-parabolic Bloch type space ${\cal B}$_α(σ) on H is the set of all solutions u of the equation (∂/∂t + (−Δ_x)^α)u = 0 with finite Bloch norm || u ||_{${\cal B}$_α}(σ) of a weight t^σ. It is known that ${\cal B}$_1/2(0) coincides with the classical harmonic Bloch space on H. We extend the notion of harmonic conjugate functions to functions in the α-parabolic Bloch type space ${\cal B}$_α(σ). We study properties of α-parabolic conjugate functions and give an application to the estimates of tangential derivative norms on ${\cal B}$_α(σ). Inversion theorems for α-parabolic conjugate functions are also given.

収録刊行物

• Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ

  Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ 65 (2), 487-520, 2013

  一般社団法人 日本数学会

キーワード

• conjugate function
• Bloch space
• parabolic operator of fractional order

詳細情報

• CRID: 1390001205116123648
• NII論文ID: 10031177289
• NII書誌ID: AA0070177X
• DOI: 10.2969/jmsj/06520487
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• NDL書誌ID: 024428791
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I024428791
• 本文言語コード: en
• データソース種別:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• 抄録ライセンスフラグ: 使用不可