Analytic operator valued function space integrals as an ${\scr L}(L_ p,L_ {pβ})$ 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 $\mathcal {S}({L_p},{L_{pβ}})$ 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 ${L_{pβ}}\;({1 < p < 2} )$ for certain functionals involving some Borel measures.References
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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