Spaces defined by the level function and their duals

• Autorzy: Gord Sinnamon
• Języki publikacji: EN

Abstrakty

EN

The classical level function construction of Halperin and Lorentz is extended to Lebesgue spaces with general measures. The construction is also carried farther. In particular, the level function is considered as a monotone map on its natural domain, a superspace of $L^p$. These domains are shown to be Banach spaces which, although closely tied to $L^p$ spaces, are not reflexive. A related construction is given which characterizes their dual spaces.

Słowa kluczowe

EN

function spaces; Hölder's inequality; Hardy's inequality; dual spaces

Kategorie tematyczne

• 26D15: Inequalities for sums, series and integrals
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994
• Tom: 111
• Numer: 1
• Strony: 19-52

Daty

wydano

1994

otrzymano

1993-07-16

Twórcy

autor

Gord Sinnamon

• Department of Mathematics, University of Western Ontario, London, Ontario, N6A 5B7, Canada,

Bibliografia

• [1] G. Bennett, Some elementary inequalities, III, Quart. J. Math. Oxford Ser. (2) 42 (1991), 149-174.
• [2] J. S. Bradley, Hardy inequalities with mixed norms, Canad. Math. Bull. 21 (1978), 405-408.
• [3] I. Halperin, Function spaces, Canad. J. Math. 5 (1953), 273-288.
• [4] G. G. Lorentz, Bernstein Polynomials, Univ. of Toronto Press, Toronto, 1953.
• [5] V. G. Maz'ja, Sobolev Spaces, Springer, Berlin, 1985.
• [6] B. Muckenhoupt, Hardy's inequality with weights, Studia Math. 44 (1972), 31-38.
• [7] H. L. Royden, Real Analysis, 2nd ed., Macmillan, New York, 1968.
• [8] G. J. Sinnamon, Operators on Lebesgue spaces with general measures, Doctoral Thesis, McMaster Univ., 1987.
• [9] G. J. Sinnamon, Weighted Hardy and Opial-type inequalities, J. Math. Anal. Appl. 160 (1991), 434-445.
• [10] G. J. Sinnamon, Interpolation of spaces defined by the level function, in: Harmonic Analysis, ICM-90 Satellite Proceedings, Springer, Tokyo, 1991, 190-193.