Geodesic
On some new estimates related with Bergman ball and Poisson integral in tubular domain and unit ball
Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 1 (2018), pp. 48-63

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We introduce new Herz type analytic spaces based on Bergman balls in tubular domains over symmetric cones and in products of such type domains. We provide for these Herz type spaces new maximal and embedding theorems extending known results in the unit disk. In addition we define new Poisson-type integral in the unit ball and extend a known classical maximal theorem related with it. Related results for such type integrals will be given.
Keywords: tubular domains over symmetric cones, Herz type spaces, Bergman type integral operators, maximal theorems, embedding theorems, unit ball.
Mots-clés : Poisson-type integral 
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     author = {R. F. Shamoyan and O. Mihi\'c},
     title = {On some new estimates related with {Bergman} ball and {Poisson} integral in~tubular domain and unit ball},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {48--63},
     publisher = {mathdoc},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2018_1_a3/}
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R. F. Shamoyan; O. Mihić. On some new estimates related with Bergman ball and Poisson integral in tubular domain and unit ball. Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 1 (2018), pp. 48-63. http://geodesic.mathdoc.fr/item/VKAM_2018_1_a3/