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A note on the spaces FP,µ*

  • Adam C. McBride (a1)

Synopsis

This note is concerned with the spaces F'p,µ of generalised functions introduced in a previous paper. A necessary and sufficient condition for an inclusion of the form

to hold is established. The case p = ∞ leads to consideration of a class G''∞µ whose simple properties are noted. Some consequences of relevance to fractional integrals and Hankel transforms are indicated.

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References

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1Kober, H.On fractional integrals and derivatives. Quart. J. Math. Oxford Ser. 11 (1940), 193211.
2McBride, A. C. A theory of fractional integration for generalised functions with applications (Edinburgh Univ. Ph.D. Thesis, 1971).
3McBride, A. C.A theory of fractional integration for generalised functions. SIAMJ. Math. Anal. 6 (1975), 583599.
4Rooney, P. G.On the ranges of certain fractional integrals. Canad. J. Math. 24 (1972), 11981216.
5Schwartz, L.Théorie des distributions (Paris: Hermann, 1966).
6Titchmarsh, E. C.Theory of Fourier integrals (Oxford: University Press, 1937).
7Trèves, F.Topological vector spaces, distributions and kernels (New York: Academic Press, 1967).
8Zemanian, A. H.Generalized integral transformations (New York: Interscience, 1968).
9Flett, T. M.On a theorem of Pitt. J. London Math. Soc. 7 (1973), 376384.
10Rooney, P. G.A technique for studying the boundedness and extendability of certain types of operators. Canad. J. Math. 25 (1973), 10901102.

A note on the spaces FP,µ*

  • Adam C. McBride (a1)

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