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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Analytic operator valued function space integrals as an ${\scr L}(L_ p,L_ {p’})$ theory
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by Kun Soo Chang and Kun Sik Ryu PDF
Trans. Amer. Math. Soc. 330 (1992), 697-709 Request permission

Abstract:

The existence of an analytic operator-valued function space integral as an $\mathcal {S}({L_p},{L_{p’}})$ theory $(1 \leq p \leq 2)$ has been established for certain functionals involving the Lebesgue measure. Recently, Johnson and Lapidus proved the existence of the integral as an operator on ${L_2}$ for certain functionals involving any Borel measure. We establish the existence of the integral as an operator from ${L_p}$ to ${L_{p’}}\;({1 < p < 2} )$ for certain functionals involving some Borel measures.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 330 (1992), 697-709
  • MSC: Primary 46G12; Secondary 28C20, 47B38, 81S40
  • DOI: https://doi.org/10.1090/S0002-9947-1992-1038013-1
  • MathSciNet review: 1038013