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On Boundedness of Weighted Hardy Operator in 
and Regularity Condition
Journal of Inequalities and Applications volume 2010, Article number: 837951 (2010)
Abstract
We give a new proof for power-type weighted Hardy inequality in the norms of generalized Lebesgue spaces 
. Assuming the logarithmic conditions of regularity in a neighborhood of zero and at infinity for the exponents 
, necessary and sufficient conditions are proved for the boundedness of the Hardy operator 
from 
into 
. Also a separate statement on the exactness of logarithmic conditions at zero and at infinity is given. This shows that logarithmic regularity conditions for the functions 
at the origin and infinity are essentially one.
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Harman, A., Mamedov, F. On Boundedness of Weighted Hardy Operator in 
and Regularity Condition.
J Inequal Appl 2010, 837951 (2010). https://doi.org/10.1155/2010/837951
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DOI: https://doi.org/10.1155/2010/837951
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