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• W1992418063 abstract "is finite; here f*(s) denotes the non-increasing rearrangement of f . Notice that this definition is a little different from the one used by other authors, since we use the measure ds instead of ds/s; we have done this for the sake of aesthetic beauty in our final results. When w 1, Aq(w) coincides with the Lebesgue space t q. When w(s) =s (1/p)-[I/q), 1 ~p<~o, we find that A~(w) is the familiar Lorentz space L p'q. With other weight functions, such as, for example, w(s)=s(1/~')-o/q)(l+llog (s)l) ~, a~R, Aq(w) becomes a space of Orlicz type, which is sometimes a good substitute for end point results for the boundedness of operators. The spaces defined by (1.1) have been extensively studied recently because of their connection to the method of real interpolation with a function parameter. In this method a pair (A0, A0 of compatible quasi-Banach spaces are given together with a function q~EB 0 and intermediate spaces, denoted by (A0, AO~,,q, 0 <q ~o ~ , are defined. (For the precise definitions see Section 2.) This theory has been developed in [6J, [11], [12] and [13J, and in particular if ~0 (t)= t o one obtains the classical real method of interpolation developed by J. L. Lions and J. Peetre (see [1], Chapter 3)." @default.
• W1992418063 created "2016-06-24" @default.
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• W1992418063 date "1991-12-01" @default.
• W1992418063 modified "2023-09-28" @default.
• W1992418063 title "Spaces of Lorentz type and complex interpolation" @default.
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• W1992418063 doi "https://doi.org/10.1007/bf02384337" @default.
• W1992418063 hasPublicationYear "1991" @default.
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