On Certain Higher Order Riccati-Type Operator Equations with Possibly Unbounded Operator Coefficients

1987 ◽  
Vol 6 (5) ◽  
pp. 409-419
Author(s):  
Tapas Mazumdar
Keyword(s):  
Unbounded Operator ◽  
Higher Order ◽  
Type Operator ◽  
Operator Equations

scholarly journals The higher order commutators of the fractional integrals on Hardy spaces

2005 ◽  
Vol 79 (1) ◽  
pp. 11-24
Author(s):  
Shunchao Long ◽  
Jian Wang
Keyword(s):  
Hardy Spaces ◽  
Fractional Integral ◽  
Higher Order ◽  
Type Operator ◽  
Fractional Integrals ◽  
Integral Type ◽  
Bmo Function

AbstractIn this paper we investigate the boundedness on Hardy spaces for the higher order commutator Tb, m generated by the BMO function b and fractional integral type operator Tτ, and establish the boundness theorems for Tτb, m from Hp1.q1.sb, m to Lp2 and to Hp2 (0 < p1 ≤ 1), and from H Ka. p1.sq1, b, m to Ka.p2q2 and to H Ka. p2q2, respectively, for certain ranges of α, p1, q1, p2, q2 and s.

Solvability of mixed type operator equations

2007 ◽  
Vol 190 (2) ◽  
pp. 1344-1352 ◽  
Author(s):  
Ibrahim Abouelfarag Ibrahim
Keyword(s):  
Mixed Type ◽  
Type Operator ◽  
Operator Equations

DEGENERATE DIFFERENTIAL-OPERATOR EQUATIONS OF HIGHER ORDER AND ARBITRARY WEIGHT

2012 ◽  
Vol 05 (02) ◽  
pp. 1250030
Author(s):  
L. Tepoyan
Keyword(s):  
Differential Operator ◽  
Existence And Uniqueness ◽  
Weighted Sobolev Spaces ◽  
Higher Order ◽  
Generalized Solutions ◽  
Operator Equations ◽  
Compactness Theorems ◽  
Arbitrary Weight ◽  
Differential Operator Equation ◽  
Degenerate Differential Operator

We consider the Dirichlet problem for a degenerate differential-operator equation of higher order with arbitrary weight-function ρ(t). We establish some embedding and compactness theorems in weighted Sobolev spaces, show existence and uniqueness of the generalized solutions. We also give a description of the spectrum for the corresponding operator.

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