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

Author 
ruslanshanin@gmail.com
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 HardyLittlewood 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 functiontheoretic 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. Weaktype 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 
209219

Volume 
42

Issue 
2

Year 
2014

Journal 
Matematychni Studii

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