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BERGMANN AND HARDY SPACES AND CONJUGATE OF THEM

Abstract

It is proved that  space is strongly notmed, and  is neither strongly notmed, nor uniformly convex. A standard form of the linear functionals over  space and over metric spaces of  0 < p £ 1, is determined.

About the Authors

Galina Y. Ryabykh
Don State Technical University.
Russian Federation


Vladimir G. Ryabykh
Southern Federal University.
Russian Federation


References

1. Danford N. Linejny`e operatory`. Obshhaya teoriya / N. Danford, Dzh. T. Shvarcz. – M., 1962. – 895 s. – In Russian.

2. Xavinson S.Ya. Osnovy` teorii e`kstremal`ny`x zadach dlya ogranichenny`x analiticheskix funkcij i ix razlichny`x obobshhenij / S.Ya. Xavinson. – M.: Izd-vo MISI, 1981. – 92 s. – In Russian.

3. Pozharskij D.A. Integral`ny`e operatory` v prostranstvax analiticheskix funkcij i blizkix k nim / D.A. Pozharskij, V.G. Ryaby`x, G.Yu. Ryaby`x. – Rostov n/D: Izdatel`skij centr DGTU, 2011. – 183 s. – In Russian.

4. Burchaev X.X. Obshhij vid linejnogo funkcionala v metricheskom prostranstve H'p, 0 < p  1 / X.X. Burchaev, V.G. Ryaby`x // Sib. mat. zhurn. – 1975. – Dep. v VINITI 17.03.75, 730–75. – In Russian.

5. Ryaby`x V.G. Linejny`e ogranichenny`e otobrazheniya v Ap / V.G. Ryaby`x // Izvestiya SKNCz VSh. – 1982. – # 3. – S. 37–41. – In Russian.

6. Ryaby`x V.G. Nekotory`e e`kstremal`ny`e zadachi v prostranstve H'p / V.G. Ryaby`x // Nauchny`e soobshheniya za 1964 g. (Seriya tochny`x i estestvenny`x nauk). – Izd-vo Rost. un-ta, 1964. – S. 74–78. – In Russian.

7. Hardy G.H. Theorems concerning mean values of analitic or armonos functions / G.H. Hardy, G.E. Littlwood // Quart. J. Math. (Oxford Ser.). – 1942. – Vol. 12. – P. 221–256.

8. Goluzin G.M. Geometricheskaya teoriya funkcij kompleksnogo peremennogo / G.M. Goluzin. – M., 1966. – 628 s. – In Russian.

9. Zigmund A. Trigonometricheskie ryady` / A. Zigmund. – T. 1. – M., 1965. – 615 s. – In Russian.


Review

For citations:


Ryabykh G.Y., Ryabykh V.G. BERGMANN AND HARDY SPACES AND CONJUGATE OF THEM. Vestnik of Don State Technical University. 2012;12(1-1):15-24. (In Russ.)

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