Xu Nie
Abstract
We characterize the sufficient and necessary conditions with respect to α and β which make the Hardy operator H n and the Hardy operator's conjugate operator H*n be bounded from L1| x |α( Rn) to Lq| x |β( Rn) with 1≤q ∞ in n-dimensional Euclidean spaces,respectively.
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We characterize the sufficient and necessary conditions with respect to α and β which make the Hardy operator H n and the Hardy operator's conjugate operator H*n be bounded from L1| x |α( Rn) to Lq| x |β( Rn) with 1≤q ∞ in n-dimensional Euclidean spaces,respectively.
Key concepts: Operator (biology), Mathematics, Bounded function, Hardy space, Euclidean geometry, Conjugate, Pure mathematics, Bounded operator