Regularity of Butterworth Re nable Functions
نویسنده
چکیده
Ai Hua FAN and Qiyu SUN Abstract Let N be the re nable function with Butterworth lter cos2N 2( cos2N 2 +sin2N 2) 1, and let sp( N) be the Sobolev exponent of N of order p (0 < p 1). It is proved in this note that there exists a constant 0 < r = rp < 1 such that ln(1 + rN) ln 2 sp( N) N ln 3 ln 2 ln(1 + 3 N) ln 2 ; (8N 1):
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