Algebras of Convolution-Type Operators with Piecewise Slowly Oscillating Data on Weighted Lebesgue Spaces

作者：Karlovich Yuri I^*

来源：Mediterranean Journal of Mathematics, 2017, 14(4): UNSP 182.

DOI：10.1007/s00009-017-0979-6

• Convolution-type operator
• piecewise slowly oscillating function
• two idempotents theorem
• symbol calculus
• Fredholmness

Let B-p,B-w be the Banach algebra of all bounded linear operators acting on the weighted Lebesgue space L-p(R, w), where p is an element of (1, infinity) and w is a Muckenhoupt weight. We study the Banach subalgebra U-p,U-w of B-p,B-w generated by all multiplication operators aI (a is an element of PSO lozenge) and all convolution operators W-0(b) (b is an element of PSOp,w lozenge), where PSO lozenge subset of L-infinity(R) and PSOp,w lozenge subset of M-p,M-w are algebras of piecewise slowly oscillating functions that admit piecewise slowly oscillating discontinuities at arbitrary points of R boolean OR {infinity}, and M-p,M-w is the Banach algebra of Fourier multipliers on L-p(R, w). For any Muckenhoupt weight w, we study the Fredholmness in the Banach algebra (Z) over bar (p,w) subset of U-p,U-w generated by the operators aW(0)(b) with slowly oscillating data a is an element of SO lozenge and b is an element of SOp,w lozenge. Then, under some condition on the weight w, we complete constructing a Fredholm symbol calculus for the Banach algebra U-p,U-w in comparison with Karlovich and Loreto Hernandez (Integr. Equations Oper. Theory 74:377-415, 2012) and Karlovich and Loreto Hernandez (Integr. Equations Oper. Theory 75:49-86, 2013) and establish a Fredholm criterion for the operators A is an element of U-p,U-w in terms of their symbols. A new approach to determine local spectra is found.

• 出版日期2017-8