Beltrami equations revisited: Marcinkiewicz exponents and Painleve-type theorem
نویسندگان
چکیده
منابع مشابه
On a Theorem of Marcinkiewicz and Zygmund
The purpose of the present paper is to prove the following result: Let F(P), P= (xi, x2, • ■ • , x„), be a function harmonic for xn >0 and such that for every point Q of a set £ of positive measure on the hyperplane x„ = 0 there exists a region contained in x„>0 limited by a cone with vertex at Q and a hyperplane x„ = const, where the function is bounded. Then except for a set of measure Zero, ...
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Therefore 0 + l)* s P + 1 mod p\ Now put t=<r + vp, (0 < c r < p 1). Then ^ = cr̂ , 0 + l)*' s (er + 1)*" mod p. Therefore (er + l)* = a + 1 mod p, (0 < a < p 1). This is relation (7) of my previous note; from this follows (1) as in the earlier treatment. Hence (1) is satisfied by all primes of the form Qn + 1. Therefore the test can be useful only when the exponent p is 3 or is of the form 6n — 1.
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ژورنال
عنوان ژورنال: Issues of Analysis
سال: 2018
ISSN: 2306-3432
DOI: 10.15393/j3.art.2018.5431