Geodesic
INTEGRAL MEANS OF THE DERIVATIVES OF BLASCHKE PRODUCTS
Glasgow mathematical journal, Tome 50 (2008) no. 2, pp. 233-249

Voir la notice de l'article provenant de la source Cambridge University Press

We study the rate of growth of some integral means of the derivatives of a Blaschke product and we generalize several classical results. Moreover, we obtain the rate of growth of integral means of the derivative of functions in the model subspace KB generated by the Blaschke product B.
DOI : 10.1017/S0017089508004175
Mots-clés : Primary: 30D50, Secondary: 32A70 
FRICAIN, EMMANUEL; MASHREGHI, JAVAD. INTEGRAL MEANS OF THE DERIVATIVES OF BLASCHKE PRODUCTS. Glasgow mathematical journal, Tome 50 (2008) no. 2, pp. 233-249. doi: 10.1017/S0017089508004175
@article{10_1017_S0017089508004175,
     author = {FRICAIN, EMMANUEL and MASHREGHI, JAVAD},
     title = {INTEGRAL {MEANS} {OF} {THE} {DERIVATIVES} {OF} {BLASCHKE} {PRODUCTS}},
     journal = {Glasgow mathematical journal},
     pages = {233--249},
     year = {2008},
     volume = {50},
     number = {2},
     doi = {10.1017/S0017089508004175},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004175/}
}
TY  - JOUR
AU  - FRICAIN, EMMANUEL
AU  - MASHREGHI, JAVAD
TI  - INTEGRAL MEANS OF THE DERIVATIVES OF BLASCHKE PRODUCTS
JO  - Glasgow mathematical journal
PY  - 2008
SP  - 233
EP  - 249
VL  - 50
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004175/
DO  - 10.1017/S0017089508004175
ID  - 10_1017_S0017089508004175
ER  - 
%0 Journal Article
%A FRICAIN, EMMANUEL
%A MASHREGHI, JAVAD
%T INTEGRAL MEANS OF THE DERIVATIVES OF BLASCHKE PRODUCTS
%J Glasgow mathematical journal
%D 2008
%P 233-249
%V 50
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004175/
%R 10.1017/S0017089508004175
%F 10_1017_S0017089508004175

[1] 1.Ahern, P. R. and Clark, D. N.On inner functions with Hp-derivative, Michigan Math. J. 21 (1974), 115–127. Google Scholar | DOI

[2] 2.Ahern, P. R. and Clark, D. N.On inner functions with Bp-derivative, Michigan Math. J. 23 (1976), 107–118. Google Scholar | DOI

[3] 3.Cohn, W. S.On the Hp classes of derivative of functions orthogonal to invariant subspaces, Michigan Math. J. 30 (1983), 221–229. Google Scholar | DOI

[4] 4.Duren, P. L. and Schuster, A., Bergman spaces, Math. Surveys and Monographs, (Amer. Math. Soc., Providence, R.I., 2004). Google Scholar | DOI

[5] 5.Duren, P. L.Theory of Hp spaces (Academic Press, 1970). Google Scholar

[6] 6.Fricain, E.Bases of reproducing kernels in model spaces, J. Operator Theory 46 (2001), 517–543. Google Scholar

[7] 7.Gotoh, Y.On integral means of the derivatives of Blaschke products, Kodai Math. J. 30 (2007), 147–155. Google Scholar | DOI

[8] 8.Havin, v. and Mashreghi, J., Admissible majorants for model subspaces of H2, Part I & II, Canadian J. Math. 55, 6 (2003), 1231–1263 and 1264–1301. Google Scholar | DOI

[9] 9.Hedenmalm, H., Korenblum, B., and Zhu, K.Theory of Bergman spaces, Graduate Text in Mathematics, No. 199 (Springer-Verlag, 2000). Google Scholar | DOI

[10] 10.Koosis, P.Introduction to Hp Spaces, Second Edition, Cambridge Tracts in Mathematics, No. 115 (Cambridge, 1998). Google Scholar

[11] 11.Kutbi, M. A.Integral means for the n'th derivative of Blaschke products, Kodai Math. J. 25 (2002), 191–208. Google Scholar | DOI

[12] 12.Linden, C. N.Hp-derivatives of Blaschke products, Michigan Math. J. 23 (1976), 43–51. Google Scholar | DOI

[13] 13.Mashreghi, J.Generalized Lipschitz functions, Comput. Methods Funct. Theory 5, (2005), 431–444. Google Scholar | DOI

[14] 14.Nikolski, N.Treatise on the shift operator (Springer-Verlag, 1986). Google Scholar | DOI

[15] 15.Protas, D.Blaschke products with derivatives in Hp and Bp, Michigan Math. J. 20 (1973), 393–396. Google Scholar

[16] 16.Protas, D.Mean growth of the derivative of a Blaschke product, Kodai Math. J. 27 (2004), 354–359. Google Scholar | DOI

Cité par Sources :