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Research articles

Extension and integral representation of the finite Hilbert transform in rearrangement invariant spaces

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Pages 783-812 | Received 17 Dec 2018, Published online: 17 Apr 2019

References

  • C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, Boston, 1988.
  • B. Blaimer, Optimal Domain and Integral Extension of Operators Acting in Fréchet Function Spaces, Logos Verlag, Berlin; Katholische Univ. Eichstätt-Ingolstadt (Ph.D. Thesis), 2017. Also available at https://zenodo.org/record/1087454.
  • J.M.F. Castillo, J.C. Diaz, and J. Motos, On the Fréchet space Lp, Manuscripta Math. 96 (1998), 219–230. doi: 10.1007/s002290050063
  • G.P. Curbera and O. Delgado, Optimal domains for L0-valued operators via stochastic measures, Positivity 11 (2007), 399–416. doi: 10.1007/s11117-007-2071-0
  • G.P. Curbera, O. Delgado, and W.J. Ricker, Vector measures: Where are their integrals? Positivity 13 (2009), 61–87. doi: 10.1007/s11117-008-2191-1
  • G.P. Curbera, S. Okada, and W.J. Ricker, Inversion and extension of the finite Hilbert transform on (–1, 1), Ann. Math. Pura Appl. 4, to appear.
  • G.P. Curbera and W.J. Ricker, Optimal domains for kernel operators via interpolation, Math. Nachr. 244 (2002), 47–63. doi: 10.1002/1522-2616(200210)244:1<47::AID-MANA47>3.0.CO;2-B
  • G.P. Curbera and W.J. Ricker, Banach lattices with the Fatou property and optimal domain of kernel operators, Indag. Math., N.S. 17 (2006), 187–204. doi: 10.1016/S0019-3577(06)80015-7
  • G.P. Curbera and W.J. Ricker, Vector measures, integration and applications, In: Positivity, K. Boulabiar, G. Buskes and A. Triki, eds., pp. 127–160, Trends in Mathematics, Birkhäuser Verlag, Basel/Berlin/Boston, 2007.
  • R. del Campo and W.J. Ricker, The Fatou completion of a Fréchet function space and applications, J. Aust. Math. Soc. 88 (2010), 49–60. doi: 10.1017/S1446788709000238
  • J. Diestel and J.J. Uhl, Jr., Vector Measures, Math. Surveys, Vol. 15, Amer. Math. Soc., Providence, R.I., 1977.
  • K. Jörgens, Linear Integral Operators, (English transl.), Pitman, Boston, 1982.
  • D.R. Lewis, Integration with respect to vector measures, Pacific J. Math. 33 (1970), 157–165. doi: 10.2140/pjm.1970.33.157
  • D.R. Lewis, On integrability and summability in vector spaces, Illinois J. Math. 16 (1972), 294–307. doi: 10.1215/ijm/1256052286
  • J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, Vol. II, Springer-Verlag, Berlin, 1979. doi: 10.1007/978-3-662-35347-9
  • W.A.J. Luxemburg and A.C. Zaanen, Riesz Spaces I, North-Holland, Amsterdam, 1971.
  • S. Okada and D. Elliot, The finite Hilbert transform in L2, Math. Nachr. 153 (1991), 43–56. doi: 10.1002/mana.19911530105
  • S. Okada, W.J. Ricker, and E.A. Sánchez-Pérez, Optimal Domain and Integral Extension of Operators: Acting in Function Spaces, Operator Theory Advances and Applications, Vol. 180, Birkhäuser, Berlin, 2008.
  • W.J. Ricker, Separability of the L1-space of a vector measure, Glasgow Math. J. 34 (1992), 1–9. doi: 10.1017/S0017089500008478
  • W.J. Ricker, Operator Algebras Generated by Commuting Projections: A Vector Measure Approach, LNM 1711, Springer, Berlin/Heidelberg, 1999. doi: 10.1007/BFb0096184
  • G.F. Stefansson, L1 of a vector measure, Le Matematiche (Catania) 48 (1993), 219–234.
  • F.G. Tricomi, Integral Equations, Interscience, New York, 1957.
  • Yu. B. Tumarkin, On locally convex spaces with basis, Dokl. Akad. Nauk SSSR 195 (1970), 1278–1281 (in Russian); English transl.: Soviet Math. Dokl. 11 (1970), 1672–1675.
  • D. van Dulst, Characterizations of Banach Spaces not Containing ℓ1, CWI Tract No. 59, Centrum voor Wiskunde en Informatica, Amsterdam, 1989.
  • A.C. Zaanen, Integration, 2nd rev. ed., North-Holland, Amsterdam, 1967.
  • A.C. Zaanen, Riesz Spaces II, North-Holland, Amsterdam, 1983.

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