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## Studia Mathematica

1995 | 116 | 3 | 255-270
Tytuł artykułu

### The one-sided minimal operator and the one-sided reverse Holder inequality

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We introduce the one-sided minimal operator, $m^+f$, which is analogous to the one-sided maximal operator. We determine the weight classes which govern its two-weight, strong and weak-type norm inequalities, and show that these two classes are the same. Then in the one-weight case we use this class to introduce a new one-sided reverse Hölder inequality which has several applications to one-sided $(A^+_p)$ weights.
Słowa kluczowe
EN
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
255-270
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-12-14
poprawiono
1995-05-31
Twórcy
autor
• Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395 U.S.A.
autor
• Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395 U.S.A.
autor
• Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395 U.S.A.
autor
• Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395 U.S.A.
Bibliografia
• [1] D. Cruz-Uribe, SFO, and C. J. Neugebauer, The structure of the reverse Hölder classes, Trans. Amer. Math. Soc. 347 (1995), 2941-2960.
• [2] D. Cruz-Uribe, SFO, C. J. Neugebauer and V. Olesen, Norm inequalities for the minimal and maximal operator, and differentiation of the integral, preprint.
• [3] J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland Math. Stud. 116, North-Holland, Amsterdam, 1985.
• [4] G. H. Hardy and J. E. Littlewood, A maximal theorem with function-theoretic applications, Acta Math. 54 (1930), 81-116.
• [5] F. J. Martín-Reyes, New proofs of weighted inequalities for the one-sided Hardy-Littlewood maximal functions, Proc. Amer. Math. Soc. 117 (1993), 691-698.
• [6] F. J. Martín-Reyes, P. Ortega Salvador and A. de la Torre, Weighted inequalities for one-sided maximal functions, Trans. Amer. Math. Soc. 319 (1990), 517-534.
• [7] F. J. Martín-Reyes, L. Pick and A. de la Torre, $(A^+_∞)$ condition, Canad. J. Math. 45 (1993), 1231-1244.
• [8] F. J. Martín-Reyes and A. de la Torre, Two weight norm inequalities for fractional one-sided maximal operators, Proc. Amer. Math. Soc. 117 (1993), 483-489.
• [9] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226.
• [10] E. Sawyer, Weighted inequalities for the one sided Hardy-Littlewood maximal functions, ibid. 297 (1986), 53-61.
• [11] J. O. Strömberg and R. L. Wheeden, Fractional integrals on weighted $H^p$ and $L^p$ spaces, ibid. 287 (1985), 293-321.
Typ dokumentu
Bibliografia
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