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Bennett, Colin

A pair of indices for function spaces on the circle. (English) Zbl 0254.46028

Trans. Am. Math. Soc. 174(1972), 289-304 (1973).
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MSC:

46J10 Banach algebras of continuous functions, function algebras
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47A20 Dilations, extensions, compressions of linear operators
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
43A15 \(L^p\)-spaces and other function spaces on groups, semigroups, etc.
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References:

[1] C. Bennett, On the harmonic analysis of rearrangement-invariant Banach function spaces, Thesis, University of Newcastle, 1971.
[2] Colin Bennett and John E. Gilbert, Homogeneous algebras on the circle. I. Ideals of analytic functions, Ann. Inst. Fourier (Grenoble) 22 (1972), no. 3, 1 – 19 (English, with French summary). · Zbl 0228.46046
[3] Colin Bennett and John E. Gilbert, Homogeneous algebras on the circle. II. Multipliers, Ditkin conditions, Ann. Inst. Fourier (Grenoble) 22 (1972), no. 3, 21 – 50 (English, with French summary). · Zbl 0228.46047
[4] D. W. Boyd, The Hilbert transform on rearrangement-invariant spaces, Canad. J. Math. 19 (1967), 599 – 616. · Zbl 0147.11302 · doi:10.4153/CJM-1967-053-7
[5] David W. Boyd, The spectral radius of averaging operators, Pacific J. Math. 24 (1968), 19 – 28. · Zbl 0173.16603
[6] David W. Boyd, Indices of function spaces and their relationship to interpolation, Canad. J. Math. 21 (1969), 1245 – 1254. · Zbl 0184.34802 · doi:10.4153/CJM-1969-137-x
[7] A.-P. Calderón, Spaces between \?\textonesuperior and \?^{\infty } and the theorem of Marcinkiewicz, Studia Math. 26 (1966), 273 – 299. · Zbl 0149.09203
[8] Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957. rev. ed. · Zbl 0078.10004
[9] G. G. Lorentz and T. Shimogaki, Interpolation theorems for operators in function spaces, J. Functional Analysis 2 (1968), 31 – 51. · Zbl 0162.44504
[10] George G. Lorentz and Tetsuya Shimogaki, Interpolation theorems for the pairs of spaces (\?^{\?},\?^{\infty }) and (\?\textonesuperior ,\?^{\?}), Trans. Amer. Math. Soc. 159 (1971), 207 – 221. · Zbl 0244.46044
[11] Wilhelmus Anthonius Josephus Luxemburg, Banach function spaces, Thesis, Technische Hogeschool te Delft, 1955.
[12] -, Rearrangement-invariant Banach function spaces, Queen’s Papers in Pure and Appl. Math., no. 10, Queen’s University, Kingston, Ont., 1967, pp. 83-144.
[13] Charles E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. · Zbl 0095.09702
[14] Tetsuya Shimogaki, An interpolation theorem on Banach function spaces, Studia Math. 31 (1968), 233 – 240. · Zbl 0172.40101
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