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1994 | 109 | 2 | 133-157
Tytuł artykułu

Integral operators and weighted amalgams

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EN
Abstrakty
EN
For large classes of indices, we characterize the weights u, v for which the Hardy operator is bounded from $ℓ^{q̅}(L^{p̅}_{v})$ into $ℓ^{q}(L^{p}_{u})$. For more general operators of Hardy type, norm inequalities are proved which extend to weighted amalgams known estimates in weighted $L^p$-spaces. Amalgams of the form $ℓ^{q}(L^{p}_{w})$, 1 < p,q < ∞ , q ≠ p, $w ∈ A_p$, are also considered and sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator and local maximal operator in these spaces are obtained.
Twórcy
  • Department of Mathematics, University Of Mons, Mons, Belgium
autor
  • Deptartment of Mathematics and Statistics, Mcmaster University, Hamilton, Ontario, Canada L8S 4K1
  • Department of Mathematics and Statistics, Wright State University, Dayton, Ohio 45435, U.S.A.
Bibliografia
  • [1] K. F. Andersen and H. P. Heinig, Weighted norm inequalities for certain integral operators, SIAM J. Math. Anal. 14 (4) (1983), 834-844.
  • [2] J. J. Benedetto, H. P. Heinig and R. Johnson, Weighted Hardy spaces and the Laplace transform II, Math. Nachr. 132 (1987), 29-55.
  • [3] G. Bennett, Some elementary inequalities III, Quart. J. Math. Oxford Ser. (2) 42 (1991), 149-174.
  • [4] J. S. Bradley, Hardy inequalities with mixed norms, Canad. Math. Bull. 21 (1978), 405-408.
  • [5] A. P. Calderón, Inequalities for the maximal function relative to a metric, Studia Math. 57 (1978), 297-306.
  • [6] C. Fefferman and E. M. Stein, Some maximal inequalities, Amer. J. Math. 93 (1971), 107-115.
  • [7] J. J. F. Fournier and J. Stewart, Amalgams of $L^p$ and $ℓ^q$, Bull. Amer. Math. Soc. 13 (1985), 1-21.
  • [8] J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland, 1985.
  • [9] F. Holland, Harmonic analysis on amalgams of $L^p$ and $ℓ^q$, J. London Math. Soc. (2) 10 (1975), 295-305.
  • [10] B. Jawerth, Weighted inequalities for maximal operators : linearization, localization and factorization, Amer. J. Math. 108 (1986), 361-414.
  • [11] V. G. Maz'ya, Sobolev Spaces, Springer, Berlin, 1985.
  • [12] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226.
  • [13] B. Opic and A. Kufner, Hardy Type Inequalities, Pitman Res. Notes Math. 219, Longman, 1990.
  • [14] G. Sinnamon, Spaces defined by their level function and their dual, preprint.
  • [15] R. Wheeden and A. Zygmund, Measure and Integral, Marcel Dekker, New York, 1977.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv109i2p133bwm
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