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On the monotonicity of some singular integral operators
Author(s) -
Junghanns Peter,
Wolfersdorf Lothar
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1605
Subject(s) - mathematics , singular integral , monotonic function , monotone polygon , logarithm , singular solution , operator (biology) , mathematical analysis , singular value , integral equation , pure mathematics , interval (graph theory) , improper integral , cauchy distribution , combinatorics , eigenvalues and eigenvectors , biochemistry , chemistry , geometry , physics , repressor , quantum mechanics , transcription factor , gene
The paper deals with the monotonicity of singular integral operators of the form Q = q S where S is the Cauchy singular integral operator on the interval (0,1) of the real axis R and q is a power or logarithmic function. Under suitable assumptions, such singular integral operators are proved to be monotone and maximal monotone inL 2spaces with power weights. Moreover, two related integral equations with weakly singular kernels of logarithmic type are studied. Copyright © 2012 John Wiley & Sons, Ltd.