A solution operator for $${\bar{\partial }}$$∂¯ on the Hartogs triangle and $$L^p$$Lp estimates

2018 ◽  
Vol 376 (1-2) ◽  
pp. 407-430 ◽  
Author(s):  
L. Chen ◽  
J. D. McNeal
Keyword(s):  
Solution Operator ◽  
Lp Estimates ◽  
Hartogs Triangle

Exponentially Convergent Approximation to the Elliptic Solution Operator

2006 ◽  
Vol 6 (4) ◽  
pp. 386-404 ◽  
Author(s):  
Ivan. P. Gavrilyuk ◽  
V.L. Makarov ◽  
V.B. Vasylyk
Keyword(s):  
Green Function ◽  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Solution Operator ◽  
Hyperbolic Operator ◽  
Elliptic Solution ◽  
Elliptic Boundary Value ◽  
Sine Family ◽  
The Green Function

AbstractWe develop an accurate approximation of the normalized hyperbolic operator sine family generated by a strongly positive operator A in a Banach space X which represents the solution operator for the elliptic boundary value problem. The solution of the corresponding inhomogeneous boundary value problem is found through the solution operator and the Green function. Starting with the Dunford — Cauchy representation for the normalized hyperbolic operator sine family and for the Green function, we then discretize the integrals involved by the exponentially convergent Sinc quadratures involving a short sum of resolvents of A. Our algorithm inherits a two-level parallelism with respect to both the computation of resolvents and the treatment of different values of the spatial variable x ∈ [0, 1].

scholarly journals On some Lp-estimates for hyperbolic equations

1992 ◽  
Vol 30 (1-2) ◽  
pp. 149-163 ◽  
Author(s):  
Mitsuru Sugimoto
Keyword(s):  
Hyperbolic Equations ◽  
Lp Estimates

Upper lp-estimates in vector sequence spaces, with some applications

1993 ◽  
Vol 113 (2) ◽  
pp. 329-334 ◽  
Author(s):  
Jesús M. F. Castillo ◽  
Fernando Sánchez
Keyword(s):  
Banach Spaces ◽  
Sequence Space ◽  
Sequence Spaces ◽  
Vector Sequence ◽  
Lp Estimates ◽  
Banach Sequence Space ◽  
Banach Sequence

In [11], Partington proved that if λ is a Banach sequence space with a monotone basis having the Banach-Saks property, and (Xn) is a sequence of Banach spaces each having the Banach-Saks property, then the vector sequence space ΣλXn has this same property. In addition, Partington gave an example showing that if λ and each Xn, have the weak Banach-Saks property, then ΣλXn need not have the weak Banach-Saks property.

scholarly journals A dual approach to Burkholder's Lp estimates

2021 ◽  
Author(s):  
Rodrigo Bañuelos ◽  
Tomasz Gałązka ◽  
Adam Osękowski
Keyword(s):  
Dual Approach ◽  
Lp Estimates
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