【摘 要】
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Let X be a ball quasi-Banach function space on Rn.In this article,we introduce the weak Hardy-type space WHx (Rn),associated with X,via the radial maximal function.Assuming that the powered Hardy-Littlewood maximal operator satisfies some Fefferman-Stein
【机 构】
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Laboratory of Mathematics and Complex Systems (Ministry of Education of China),School of Mathematica
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Let X be a ball quasi-Banach function space on Rn.In this article,we introduce the weak Hardy-type space WHx (Rn),associated with X,via the radial maximal function.Assuming that the powered Hardy-Littlewood maximal operator satisfies some Fefferman-Stein vector-valued maximal inequality on X as well as it is bounded on both the weak ball quasi-Banach function space WX and the associated space,we then es-tablish several real-variable characterizations of WHx (Rn),respectively,in terms of various maximal functions,atoms and molecules.As an application,we obtain the boundedness of Calderón-Zygmund operators from the Hardy space Hx (Rn) to WHx (Rn),which includes the critical case.All these results are of wide applications.Particularly,when X :=Mpq(Rn) (the Morrey space),X :=L(p)(Rn) (the mixed-norm Lebesgue space) and X :=(EqΦ)t(Rn) (the Orlicz-slice space),which are all ball quasi-Banach function spaces rather than quasi-Banach function spaces,all these results are even new.Due to the generality,more applications of these results are predictable.
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