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Bl p;; a;;(G). The smothness of solution of one class quasielliptic equations are studied. sn this p per oth differenti l nd differen eEdifferenti l properties of fun tions elonging to interse tion of the sp es Bl p;; a;;@ G; A; a I; P;:::; N nd the smoothness of solution of one l ss of qu siellipti equ tions re studiedF vet G & Rn e dom in s tisfying the ondition of exi le Ehorn introdu ed y yF Ffesov in the p per I nd let p Pi; IAnY Pi; Iy; l P@ H; IAn; a I; P;:::; NY a Ph; I n Y Pi; Iy t I a minfI; tg: essume for ny x PRn nd t> H