On a generalization of the Fefferman-Stein theorem (in Russian) |
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| Author |
ruslanshanin@gmail.com
Odessa I. I. Mechnikov National University
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| Abstract |
We investigate the conditions under which membership of the maximal function of C. Fefferman and E. M. Stein to the class $\varphi (L)$ implies that the Hardy--Littlewood function belong to the same class. We obtain the best possible in some sense, conditions on the function $\varphi$ defining these classes.
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| Keywords |
Hardy-Littlewood maximal function; Fefferman-Stein maximal function; equimeasurable rearrangement
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| DOI |
doi:10.30970/ms.42.2.209-219
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| Reference |
1. Hardy G.H., Littlewood J.E. A maximal theorem with function-theoretic applications// Acta Math. -
1930. - V.54. - P. 81-116.
2. Fefferman C., Stein E.M. Hp spaces of several variables// Acta Math. - 1972. - V.129. - P. 137?139. 3. Korenovskii A.A. Properties of functions defined in terms of the mean oscillations: dis. . . kand. phis.-math. nauk: 01.01.01 - Odessa, 1988. - 121 p. (in Russian) 4. Kolyada V.I. Rearrangements of functions and embedding theorems// Usp. Mat. Nauk. - 1989. - V.44, №5(269). - P. 61-95. (in Russian) 5. Bennett C., Sharpley R. Weak-type inequalities for $H^p$ and BMO// Proc. Sympos. Pure Math. - 1979. - V.35, Part1. - P. 201-229. 6. Kolyada V.I. On imbedding in classes '(L)// Isv. AN SSSR. - 1975. - V.39, №2. - P. 418?437. (in Russian) |
| Pages |
209-219
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| Volume |
42
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| Issue |
2
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| Year |
2014
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| Journal |
Matematychni Studii
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| Full text of paper | |
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