Convolution theorems with weights
HTML articles powered by AMS MathViewer
- by R. A. Kerman PDF
- Trans. Amer. Math. Soc. 280 (1983), 207-219 Request permission
Abstract:
Analogues of Youngโs Inequality and the Convolution Theorem are shown to hold when the ${L_p}$ and $L(p,q)$ spaces have underlying measure defined in terms of power weights.References
- A. P. Blozinski, On a convolution theorem for $L(p,q)$ spaces, Trans. Amer. Math. Soc. 164 (1972), 255โ265. MR 415293, DOI 10.1090/S0002-9947-1972-0415293-1
- A.-P. Calderรณn, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113โ190. MR 167830, DOI 10.4064/sm-24-2-113-190 G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge Univ. Press, London, 1934.
- Richard A. Hunt, On $L(p,\,q)$ spaces, Enseign. Math. (2) 12 (1966), 249โ276. MR 223874
- G. G. Lorentz, Some new functional spaces, Ann. of Math. (2) 51 (1950), 37โ55. MR 33449, DOI 10.2307/1969496 G. O. Okikiolu, Aspects of the theory of bounded integral operators on ${L^p}$-spaces, Academic Press, New York, 1970.
- Richard OโNeil, Convolution operators and $L(p,\,q)$ spaces, Duke Math. J. 30 (1963), 129โ142. MR 146673
- E. M. Stein and G. Weiss, Interpolation of operators with change of measures, Trans. Amer. Math. Soc. 87 (1958), 159โ172. MR 92943, DOI 10.1090/S0002-9947-1958-0092943-6
- E. M. Stein and Guido Weiss, An extension of a theorem of Marcinkiewicz and some of its applications, J. Math. Mech. 8 (1959), 263โ284. MR 0107163, DOI 10.1512/iumj.1959.8.58019
- Leonard Y. H. Yap, Some remarks on convolution operators and $L(p,\,q)$ spaces, Duke Math. J. 36 (1969), 647โ658. MR 249943
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 280 (1983), 207-219
- MSC: Primary 42B99; Secondary 42A85
- DOI: https://doi.org/10.1090/S0002-9947-1983-0712256-0
- MathSciNet review: 712256