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# 1. Introduction. Let Ω be an open bounded subset of C, and let a be a point in Ω. Suppose that a function z 7→ G

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INSTITUTE OF MATHEMATICS POLISH ACADEMY OF SCIENCES

WARSZAWA 1995

z→w

0

z→w

2

(2)

1

2

1

2

2

1

n

n

n

1

2

2

1

2

(3)

12

2

n

c

n

c

n

n

n

n

B

n

−1

(4)

n

n

n

n

n

0

n

m

0

0

0

0

0

0

0

j

j∈N

n

j

j→∞

j

1

(5)

m

j=1

−1

j

j+1

j+1

j

1

m+1

1

m+1

n

λ→0 λ6=0

n

2

(6)

2

∂z2u

j∂ ¯zk

2

n

∂z2u

j∂ ¯zk

n

c

c

c

n

c

c

n

c

c

n−times

2

c

n

n

2

j

k

n

n

2

c

n

0

0

n

2

0

2

j

k

a

2

2

j

k

c

n

a

2

c

n

n

1

m

1

m

1

m

1

n

j

j

1

n

p

1

n

(7)

1

n

p

n

p

1

n

n

n

1

2

n1

n2

1

1

2

2

1

2

1

1

2

2

1

2

1

2

1

2

n

1

k

2

c

1

c

k

j

c

1

c

j−1

c

j+1

c

k

c

n

1

n

2

K

c

1

c

n

1

L

n

L

L

c

(8)

1

n

loc

c

1

c

k

## R

c

1

c

k

k

c

1

c

k−1

c

c

n

n

j

j∈N

loc

loc

c

j

n

c

n

n

c

n

n

j

j∈N

loc

c

j

n

n

loc

n

(9)

j

j∈f N

loc

c

j

n

j∈N

loc

c

n

c

n

n

n

c

n

n

a

a

n

−1

−1

z→a

c

n

c

n

c

n

n

c

n

n

a

a

n+1

P (0,1)

2

1

(10)

1

2

n1

n2

1

2

1

2

1

2

1

1

1

2

2

2

1

1

2

2

1

2

1

2

1

1

1

2

2

2

1

2

1

2

c

n1+n2

n1+n2

c

n1+n2

1

2

c

n1+n2

n1+n2

z

1

k

1

k

j=1,...,k

j

j

j

1

k

1

k

1

n

n

j

(11)

j=1,...,n

j

j

j

j

j

j

j

j

j

j

j

j

j

j

n

n

n

n

−1

−1

n

n

n

n

n

p1

np

1

n

n

n

n

n

−1

−1

p

−1

p

−1

−1

jk

n

(12)

1

n

1

n

1

21

2

31

32

3

n1

n2

n3

n

1(d+1)(n−1)

2(d+1)(n−1)

3(d+1)(n−1)

n(d+1)(n−1)

1

n

n

−1

n

n

1

n

1

n

1

n

1

n

n

1

n

x1

xn

1

n

n

−∞

1

n

1

n

1

n

1

1

n

n

1

n

n

n

n

n

n

(13)

1

n

1

n

n

n

n

n

1

2

1

2

ω

M(c)

ω1

ω2

1

2

n

n

ω

n

1

2

1

2

z→a

z∈ω

ω

0

n

1

0

0

z→a

z∈ω0

ω0

n

1

n

n

j=1

j

j

1

n

n

1

n

n

ω

(14)

n

1

2

1

2

0

0

ω

0

ω

0

ω

0

x→x0

x∈ω

ω

0

1

0

0

n

0

0

ω

1

0

0

1

0

0

0

0

0

0

ω

2

n

2

ω

ω

2

t

1−t

t

1−t

2

1

2

3

4

1

log D/ log C

2

log B/ log A

3

4

1

2

3

(15)

1

2

BA

DC

BA

DC

3

log D

log C

log Blog A

log Alog B

log Dlog C

4

−2

−1

2

2

3

−2

−1

1

2

3

4

2

2

−2

−1

−2

−1

2

2

1

2

log B/ log A

3

log B/ log A

4

1

2

3

4

2

3

4

(16)

2

1

2

3

1

2

−1

2

2

2

2

3

2

wz

2

1

2

3

2

0

1

0

2

2

2

2

1

2

2

11

2

n

D

(17)

n

n

D

D

D

n

D

(18)

n

f D

h(Ω)

D

1

2

h(Ω)

1

2

1

2

D

1

2

1

2

n

n

n

(19)

(20)

n

### parabolique et applications, Math. Scand. 69 (1991), 89–126.

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