On Boundedness of Weighted Hardy Operator in Open image in new window and Regularity Condition
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We give a new proof for power-type weighted Hardy inequality in the norms of generalized Lebesgue spaces Open image in new window . Assuming the logarithmic conditions of regularity in a neighborhood of zero and at infinity for the exponents Open image in new window , necessary and sufficient conditions are proved for the boundedness of the Hardy operator Open image in new window from Open image in new window into Open image in new window . 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 Open image in new window at the origin and infinity are essentially one.
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