# On a generalization of the Fefferman–Stein theorem (in Russian)

Author
Odessa I. I. Mechnikov National University
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.
Keywords
Hardy–Littlewood maximal function; Fefferman–Stein maximal function; equimeasurable rearrangement
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, ¹5(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, ¹2. – P. 418–437. (in Russian)

Pages
209-219
Volume
42
Issue
2
Year
2014
Journal
Matematychni Studii
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