I n t h e s e a r t i c l e s many i m p o r t a n t p r o p e r t i e s o f t h e i n d i c a t e d c l a s s e s h a v e been f o u n d . The c l a s s e s HP(a) i n c l u d e t h e s e t o f h o l o m o r p h i c f u n c t i o n s in t h e d i s k t h a t a d m i t power g r o w t h n e a r t h e b o u n d a r y o f t h e d i s k . The c l a s s e s o f t h e l a s t t y p e a r i s e in v a r i o u s p r o b l e m s o f a n a l y s i s . Thus , e . g . , by v i r t u e o f t h e r e s u l t s o f [3] we can e a s i l y p r o v e t h a t e a c h f u n c t i o n of the class HP(u) in the generalized sense has boundary values on the unit circle. We can represent each generalized function on the unit circle in the form of the boundary value of a certain function from the class HP(a) + HP(a). We should dwell specially on the properties of the kernels