一类带特殊象征类的拟微分算子的L^p有界性

THE L^p-BOUNDEDNESS OF PSEUDO-DIFFERENTIAL OPERATORS WITH A SPECIAL SYMBOLS

国内外许多数学家研究带象征类S的拟微分算子的L^P有界性时,都有一个共同的假设条件,即m≤0,人们自然关注当m>00时,L^P有界性是否成立?为了回答这个问题,本文将给出一类特殊的拟微分算子的L^P(1<p<∞)有界性.

L^p-boundedness of pseudo-differential operators with the symbol S_(ρb)~m was discussed by many mathema- tians both at home and abroad, but there is a congruent hypothesis in ≤0.1 It seems understandable to ask whether the L^p -boundedness is right when in >0. For the purpose of this problem, the pseudo-differential operators with a special symbol are studied in this paper.