Necessary and sufficient conditions for weighted Orlicz class inequalities for maximal functions and singular integrals. II. (English) Zbl 0858.42011

This is an interesting paper on integral operators on homogeneous type spaces. For singular kernel operators \(Kf(x)=\lim_{\varepsilon\to 0} \int_{d(x,y)>\varepsilon} k(x,y)f(y)d\mu\), criteria are found for weak-type Orlicz class inequalities. Calderón-Zygmund operators are treated as well. Of particular interest are the characterizations of strong type inequalities for singular integrals and maximal functions. Applications to classical operators such as the Hilbert transform are pointed out.
[See also Part I, same journal 2, No. 4, 361-384 (1995; Zbl 0836.42012)].
Reviewer: L.Pick (Praha)


42B25 Maximal functions, Littlewood-Paley theory
26D15 Inequalities for sums, series and integrals
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47G10 Integral operators


Zbl 0836.42012
Full Text: EuDML EMIS


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