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- W2076616083 abstract "We show that the Hardy operator $$ Hf(x) = frac{1}{x}mathop {int }limits_0^x f(t)dt $$ from $$ L_{{text{dec}},w}^{p),theta } $$ (I) to $$ L_w^{p),theta } $$ (I), 0 < p < ∞, θ > 0, I = (0, 1), is bounded if and only if the weight w belongs to the well–known class Bp restricted to the interval I. This result is applied to derive a similar assertion for the Riemann–Liouville fractional integral operator and to establish criteria for the boundedness of the Hardy–Littlewood maximal operator in the weighted grand Lorentz space $$ Lambda_w^{p),theta } $$ . Bibliography: 23 titles." @default.
- W2076616083 created "2016-06-24" @default.
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- W2076616083 date "2011-10-21" @default.
- W2076616083 modified "2023-10-18" @default.
- W2076616083 title "Weighted criteria for the hardy transform under the B p condition in grand lebesgue spaces and some applications" @default.
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- W2076616083 doi "https://doi.org/10.1007/s10958-011-0574-5" @default.
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