Weighted Modular Inequalities for Hardy Type Operators |
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Authors: | Lai Qinsheng |
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Affiliation: | Department of Mathematics and Statistics, McMaster University Hamilton, Ontario L8S 4K1, Canada, email: laiq{at}icarus.math.mcmaster.ca |
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Abstract: | Given weight functions , w, and v, the weighted modular inequality is characterized. Here Qis a strictly increasing function with Q(0) = 0, Q() = and2Q(x) Q(C x), P is a Young's function, and T is the Hardy operatoror a Hardy type operator. In particular, a characterizing conditionfor the Hardy type operator to map Lp(w) to Lq(v) when 0 <q < 1 p < is deduced. In addition, a new proof for theMaz'ja-Sinnamon theorem is given, and weighted Lorentz norminequalities for Hardy type operators are established. 1991Mathematics Subject Classification: primary 26D15, 42B25; secondary26A33, 46E30. |
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Keywords: | the Hardy operator Hardy type operator weighted modular inequality |
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