Distance from Bloch-type functions to the analytic space \(F(p, q, s)\). (English) Zbl 1474.42099

Summary: The analytic space \(F(p, q, s)\) can be embedded into a Bloch-type space. We establish a distance formula from Bloch-type functions to \(F(p, q, s)\), which generalizes the distance formula from Bloch functions to BMOA by Peter Jones, and to \(F(p, p - 2, s)\) by Zhao.


42B35 Function spaces arising in harmonic analysis
30D45 Normal functions of one complex variable, normal families
Full Text: DOI


[1] Timoney, R., Bloch functions in several complex variables. I, The Bulletin of the London Mathematical Society, 12, 4, 241-267 (1980) · Zbl 0416.32010
[2] Timoney, R., Bloch functions in several variables, Journal für die Reine und Angewandte Mathematik, 319, 1-22 (1980) · Zbl 0425.32008
[3] Zhao, R. H., On a general family of function spaces, Annales Academiæ Scientiarum Fennicæ Mathematica Dissertationes, 105, 1-56 (1996)
[4] Aulaskari, R.; Lappan, P., Criteria for an analytic function to be Bloch and a harmonic or meromorphic function to be normal, Complex Analysis and Its Applications. Complex Analysis and Its Applications, Pitman Research Notes in Mathematics 305, 136-146 (1994), Harlow, UK: Longman Scientific & Technical, Harlow, UK · Zbl 0826.30027
[5] Aulaskari, R.; Stegenga, D. A.; Xiao, J., Some subclasses of BMOA and their characterization in terms of Carleson measures, The Rocky Mountain Journal of Mathematics, 26, 2, 485-506 (1996) · Zbl 0861.30033
[6] Aulaskari, R.; Xiao, J.; Zhao, R. H., On subspaces and subsets of BMOA and UBC, Analysis, 15, 2, 101-121 (1995) · Zbl 0835.30027
[7] Rättyä, J., n-th derivative characterizations, mean growth of derivatives and \(F\)( p, q, s), Bulletin of the Australian Mathematical Society, 68, 405-421 (2003) · Zbl 1064.30027
[8] Zhao, R. H., On logarithmic Carleson measures, Acta Scientiarum Mathematicarum, 69, 3-4, 605-618 (2003) · Zbl 1050.30024
[9] Zhao, R. H., Distances from Bloch functions to some Möbius invariant spaces, Annales Academiæ Scientiarum Fennicæ Mathematica, 33, 303-313 (2008) · Zbl 1147.30024
[10] Ghatage, P. G.; Zheng, D. C., Analytic functions of bounded mean oscillation and the Bloch space, Integral Equations and Operator Theory, 17, 4, 501-515 (1993) · Zbl 0796.46011
[11] Lou, Z.; Chen, W., Distances from Bloch functions to \(Q K\)-type spaces, Integral Equations and Operator Theory, 67, 2, 171-181 (2010) · Zbl 1208.30034
[12] Tjani, M., Distance of a BLOch function to the little BLOch space, Bulletin of the Australian Mathematical Society, 74, 1, 101-119 (2006) · Zbl 1101.30035
[13] Xu, W., Distances from Bloch functions to some Möbius invariant function spaces in the unit ball of \(C^n\), Journal of Function Spaces and Applications, 7, 91-104 (2009) · Zbl 1182.32003
[14] Xiao, J., Geometric \(Q_p\) Functions. Geometric \(Q_p\) Functions, Frontiers in Mathematics (2006), Basel, Switzerland: Birkhäauser, Basel, Switzerland · Zbl 1104.30036
[15] Xiao, J.; Yuan, C., Analytic campanato spaces and their compositions · Zbl 1333.30068
[16] Zhu, K., Operator Theory in Function Spaces (2007), Providence, RI, USA: American Mathematical Society, Providence, RI, USA
[17] Ortega, J. M.; Fàbrega, J., Pointwise multipliers and corona type decomposition in BMOA, Annales de l’institut Fourier, 46, 1, 111-137 (1996) · Zbl 0840.32001
[18] Qiu, L.; Wu, Z., s-Carleson measures and function spaces, Report Series, 12 (2007), University of Joensuu, Department of Physics and Mathematics · Zbl 1157.32008
[19] Arcozzi, N.; Blasi, D.; Pau, J., Interpolating sequences on analytic besov type spaces, Indiana University Mathematics Journal, 58, 3, 1281-1318 (2009) · Zbl 1213.30069
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.