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Journal of the London Mathematical Society 1987 s2-35(3):489-498; doi:10.1112/jlms/s2-35.3.489
© 1987 by London Mathematical Society
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© Oxford University Press

Hardy–Landau–Littlewood Inequalities for Fractional Derivatives in Weighted Lp Spaces

Rhonda J. Hughes

Department of Mathematics, Bryn Mawr College Bryn Mawr, Pennsylvania 19010, USA

The inequality of Hardy, Landau and Littlewood is established in weighted Lp spaces, for weights satisfying Muckenhoupt's (Ap) condition. That is, for f isin Dom (D{gamma}), where D{gamma} denotes the {gamma}th fractional derivative acting in Formula(0, {infty}),

Formula
,for 0 < {alpha} < {gamma}, and Formula. In addition, we show that the indefinite integral possesses a strongly continuous group of imaginary powers in Formula(0, {infty}).


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