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It is concerned with the continuity of the Hardy-Little wood maximal function between the classical Lebesgue spaces or the Orlicz spaces. A new approach to the continuity of the Hardy-Littlewood maximal function is presented through the observation that the continuity is closely related to the existence of solutions for a certain type of first order ordinary differential equations. It is applied to verify the continuity of the Hardy-Littlewood maximal function from $L^p({\mathbb{R}}^n)$ to $L^q({\mathbb{R}}^n)$ for 1 ${\leq}$ q < p < ${\infty}$.
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참고문헌 (4)
참고문헌 신청
R. Adams / 2003 / Sobolev spaces / Academic press
G. H. Hardy / 1930 / A maximal theorem with function-theoretic applications / Acta Math. 54:81~116
A. D. Melas / 2003 / The best constant for the centered Hardy-Littlewood maximal inequality / Annals of Mathematics 157:647~688
E. M. Stein / 1993 / Harmonic analysis; Real-variable methods, orthogonality, and osillatory integrals
G. H. Hardy / 1930 / A maximal theorem with function-theoretic applications / Acta Math. 54:81~116
A. D. Melas / 2003 / The best constant for the centered Hardy-Littlewood maximal inequality / Annals of Mathematics 157:647~688
E. M. Stein / 1993 / Harmonic analysis; Real-variable methods, orthogonality, and osillatory integrals
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