TY - JOUR
T1 - Boundedness and fredholmness of pseudodifferential operators in variable exponent spaces
AU - Rabinovich, Vladimir
AU - Samko, Stefan
N1 - Funding Information:
Supported by CONACYT Project No.43432 (Mexico), the Project HAOTA of CEMAT at Insti-tuto Superior Técnico, Lisbon (Portugal) and the INTAS Project “Variable Exponent Analysis” Nr.06-1000017-8792.
PY - 2008/4
Y1 - 2008/4
N2 - We prove a statement on the boundedness of a certain class of singular type operators in the weighted spaces Lp(•)(ℝn, w) with variable exponent p(x) and a power type weight w, from which we derive the boundedness of pseudodifferential operators of Hörmander class S 0 1,0 in such spaces. This gives us a possibility to obtain a necessary and sufficient condition for pseudodifferential operators of the class OPS m 1,0 with symbols slowly oscillating at infinity, to be Fredholm within the frameworks of weighted Sobolev spaces H ws,p(•)(ℝn) with constant smoothness s, variable p(•)-exponent, and exponential weights w.
AB - We prove a statement on the boundedness of a certain class of singular type operators in the weighted spaces Lp(•)(ℝn, w) with variable exponent p(x) and a power type weight w, from which we derive the boundedness of pseudodifferential operators of Hörmander class S 0 1,0 in such spaces. This gives us a possibility to obtain a necessary and sufficient condition for pseudodifferential operators of the class OPS m 1,0 with symbols slowly oscillating at infinity, to be Fredholm within the frameworks of weighted Sobolev spaces H ws,p(•)(ℝn) with constant smoothness s, variable p(•)-exponent, and exponential weights w.
KW - Fredholmness
KW - Hörmander class
KW - Pseudodifferential operators
KW - Singular operators
KW - Variable exponent
KW - generalized Lebesgue space
UR - http://www.scopus.com/inward/record.url?scp=43749104657&partnerID=8YFLogxK
U2 - 10.1007/s00020-008-1566-9
DO - 10.1007/s00020-008-1566-9
M3 - Artículo
SN - 0378-620X
VL - 60
SP - 507
EP - 537
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
IS - 4
ER -