SCIENTIFIC ABSTRACT GEGELIA, T.G. - GEGESHIDZE, G.A.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000514610008-6
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: August 23, 2000
• Sequence Number: 8
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

GBGIKLIA. T.G.
Omm
I.I. Privaloyle basic lema for space potentials. Soob. AN
Grus.SSR 18 no.3:257-264 Mr '57. (KZRA 10:7)
I. Aimdevilys nauk Grusinskay SSR, Tbilleskly zateaRtichoskly
institut Imnj A.K. Rasmdse. '
(Potential, Theory d)

GJGILIA,, T.G.
I-MMMOMISM"
Proportion of ,,srtain clamses of coninuous f=ctions associated
with Hilbert transform in IIA. Soob. AN Gruz. 3M 19 no,3t-257-
261 s.-957. (mm 1115)
1, AkR&nlya amak OmInskoy 33R, ThIliaskly mtematicheddy
Institut in. A6N. lkzmdze. Predstavlano chlonoso.-korrompondentom
Akadeaft NP. Takuae
(Vunctions,, Continuous)

GEGELIA, T.G. ,
-
..J., , I-v
Boundednons of singular operators. Scob. Mi Gruz.SSR XIO no.5:
517-523 It '58- (MIRA 11:10)
1. AN GrusSSR. Tbillsoldy mutemtichoskiy inntitut in. L.M.
Razmdze. Prodstavleno chlenon-korres pondentom Akadomil N.P.Vakua.
(Operators (Mathematics))

GIGSLU, T. G.
Behavior of generalized potential near the boundar7 of an
integration set. Tru4 Hat.inst.Al Gruz.SSR 26:189-193
139. (M MA 13:6)
Ofunctions, Analytic)

42
29861
S/044/61/000/007/0!4/055
~ ~12 6 O~ C1J1/C222
AUTBORo Gogellaq T.G.
TITLEs Differential properties of some integral manifolds
PERIODICAM Referativnyy shurnal.Matematika, no. 7, 1961, 79,
abstract T B 388. ("Tr. Tbilinak. matem. in-ta. AN Gruz SSR",
1959t 269 195-225)
TEXTe Lot P(xiv x2""*Oxn) 9 Q(yl* Y2*""Yn) be points of the
n-disonsional *pact En, r(P,q) be the distance between P and qbe
the unit vector of Q in the direction P I R(Q) be a continuous function
the integral over the unit sphere of which is equal to zeros,~ FL(Q)d(r -0.
In the paper the author gives a number of results on the differential
properties of the function
(P) IrL(Q)K(P.M f(q)dq
rn(P,Q)
Card I/S.
i J,

Difforen'tial properties of some
29861
S/044/61/000/007/034/055
see C111/C222
in dependence on the differential properties of f(Q) and under certain
restrictions for the kernel K(PqQ). As an example we give a theorem for
which we promise the following definitionst It holds K(P,Q)6 T ir in
*very bounded closed not Dt it holds uniformly with respect to Pt
lin K(P.Q) - K(P.P) dQ 0
$'*0 1r(1 r) rn(F,Q)
here V(P,S) is the sphere with the radius and the center P. It holds
,,0) if K(POQ) in measurable in Q for every P and
K( Pt Q) C- I (p>0 pG>
if for every bounded not D' there exists a constant c - c (Dt, p) so
that for P&D' it holds i
f S lz(P.Q)IP dQ 1/p 14 0
in.
W0000
Card 215

43
29801
S/044J61/000/007/034/055
Differential proportion of some ... C111/0222
It holds K(ptq) eA" if K(p,q)6 TAL and if for every bounded sot
Pt a, P OG
DO there exists an increasing function )#1t) so that lim )0(t) - 0 and
t-1.0
sup K(P10q) - K(P2 Q I e- 9 (-~) F (Q)
P 1 0 P2 4W Dr(P, 0 P 2 ) -C 9
where F(Q)fi L Lot i !!L-ikKn) be integers, and lot i
Jk3 _ [.H(Pgq)j [k-1] + [H (p, q [k- I I
2xik 7yk (2)
[u(p9q)] 101 - jj(pq) (k - 1,2,...,m)
Theorem s If the functions K(P#Q), [K(P,Q)]f'11 .... [K(P,Q)I[ M' belong
to the also@ VIP and the functions
qqn
Card 3/T

S~04YO 000/007/034/055
Differential proportion of mono 60* C 11 C22~
f(p) , If(P-I ?a f(p)
im
belong to the class L rIT (p >1 I/p + I/q - 1) then the function
Pon
tf(P) defined by (1) in existing and continuous on En , there exist its
continuous partial derivatives
x .00~x
i
and
[X(P,Q)f(Q)Jfkl dQ (k
7xil.*. ik ~n rn(P,Q)
Card

44
29861
S/044/61/000/007/034/055
Differential properties of some ... C111/C222
where Ll(p,,q)]Ckl Is asloulated with H - If according to the formula
Me Other analogous theorems are proved.
[Abstractor's note i Complete translation.1
Card

89008
3/020
gatoo /60/135/004/001/037
14.4m C1 I I/C222
AUTSORt G*xelia. T.0.
TITLIs Composition of Singular lernals
PERIODICALt Doklady Akadenii nauk SSSR,196o, Vol-135, To-4, pp-767-770
TZXTs Lot xt yp tt x19 y1pose be points of the Suclidean I M+11 `(ZqY)
be the distance between x and yj qx(y,t) - min fr(z,y), r(i,t)). a denotes
constants Independent of the principal variables. Let S be a closed
a-limensional Lyapunov surface in 9,+,* On(S#S) lot functions K I(Xty)
and K2(x' y) be defined being continuous on (S,S),with a possible exception
of the points (X,X) and satisfying the following conditionst
10. jK,(x,y)j4.f,(r(z,y))p IK 2(10Y)1 1452 (r(xgy)).
0
2
0
3 Ix 2(K' #y)-K 2(z"'Y)11'