Boundedness of n-Multiple Discrete Hardy Operators with Weights for 1<q<p<∞
We find necessary and sufficient conditions on weighted sequences ωi, i=1,2,…,n-1, u, and v, for which the operator (Sn-1f)i=∑k1=1iω1,k1⋯∑kn-1=1kn-2ωn-1,kn-1∑j=1kn-1fj,i≥1, is bounded from lp,v to lq,u for 1<q<p<∞.
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/121767 |
| Summary: | We find necessary and sufficient conditions on weighted sequences ωi, i=1,2,…,n-1, u, and v, for which the operator (Sn-1f)i=∑k1=1iω1,k1⋯∑kn-1=1kn-2ωn-1,kn-1∑j=1kn-1fj,i≥1, is bounded from lp,v to lq,u for 1<q<p<∞. |
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| ISSN: | 0972-6802 1758-4965 |