On the Boundedness of Dyadic Hardy and Hardy-Littlewood Operators on the Dyadic Spaces H and BMO

R. Bellmann, A note on a theorem of Hardy on Fourier coefficients, Bull. Amer. Math.Soc., 50(1944), 741–744. Dang Vu Giang and F. MÓricz TheCesàro operator is bounded on the Hardy space H1, Acta Sci.Math. (Szeged ), 61(1995), 535–544. T. Eisner The dyadic Cesàro operators, Acta Sci.Math.(Szeged ), 64(1998), 201–214. D. Garnet, Ograniqennye analitiqeskie funkcii, Mir (Mo kva, 1984). B.I. Golubov, A.V. Efimov, i V.A. Skvorcov, R dy i preobrazovani Uolxa.Teori i primenen i, Nauka (Mokva, 1987). B.I. Golubov, Ograniqennost operatorov Hardi i Hardi –Littlvuda v prostranstvah Re H1 i BMO, Matem. sb., 188(1997), 93–106. B.I. Golubov, Analog odno i teoremy Titqmarxa dl preobrazovani Fur e, Matem. sb., 189(1998), 69–86. B.I. Golubov, O dvoiqnyh analogah operatorov Hardi i Hardi –Littlvuda, Sib. Matem. urn., 40(1999), 1244–1252. G.G. Hardi, D.E. Littl vud i G. Polia, Neravenstva, IL (Moskva, 1948). G.H. Hardy Notes on some points in the integral calculus, Messenger Math., 58(1928), 50–52. F. John and L. Nirenberg On functions of bounded mean oscillation, Comm. Pure Appl. Math., 35(1961), 415–426. S.G. Kre in,.I. Petunin i E.I. Semenov, Interpol ci line inyh operatorov, Nauka (Mo kva, 1978). D. Sarason, Functions of vanishing mean oscillation, Trans. Amer. Math. Soc., 207(1975), 391–405. F. Schipp, W. R. Wade, and P. Simon, Walsh series.An introduction to dyadi harmoni analysis, Adam Hilger (Bristol–New York, 1990). A. G. Siskakis, Composition semigroups and the Cesàro operator on H p, J. London Math. Soc., 36(2)(1987), 153–164. A. G. Siskakis, The Cesàro operator is bounded on H p, Proc. Amer. Math. Soc., 110(1990), 461–462. K. Stempak, Cesàro averaging operators, Proc. Royal Soc. Edinbourgh, 124(1994), 121–126. A. Torchinsky, Real-variable methods in harmonic analysis, Academic Press (New York, 1986).