Atomic Decompositions of Hardy Spaces with Variable Exponents and its Application to Bounded Linear Operators

2013 ◽  
Vol 77 (1) ◽  
pp. 123-148 ◽  
Author(s):  
Yoshihiro Sawano
Keyword(s):  
Hardy Spaces ◽  
Linear Operators ◽  
Variable Exponents ◽  
Bounded Linear Operators ◽  
Atomic Decompositions ◽  
Bounded Linear

A note on Hardy spaces and bounded linear operators

2018 ◽  
Vol 25 (1) ◽  
pp. 73-76
Author(s):  
Pablo Rocha
Keyword(s):  
Linear Operator ◽  
Hardy Spaces ◽  
Bounded Linear Operator ◽  
Atomic Decomposition ◽  
Bounded Operator ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear

AbstractIn this note we show that if{f\in H^{p}(\mathbb{R}^{n})\cap L^{s}(\mathbb{R}^{n})}, where{0<p\leq 1<s<\infty}, then there exists a{(p,\infty)}-atomic decomposition which converges tofin{L^{s}(\mathbb{R}^{n})}. From this result, we obtain that a bounded linear operatorTon{L^{s}(\mathbb{R}^{n})}can be extended to a bounded operator from{H^{p}(\mathbb{R}^{n})}into{L^{p}(\mathbb{R}^{n})}if and only ifTis bounded uniformly in{L^{p}}norm on all{(p,\infty)}-atoms. A similar result is also obtained from{H^{p}(\mathbb{R}^{n})}into{H^{p}(\mathbb{R}^{n})}.

Cline’s formula for g-Drazin inverses in a ring

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2249-2255
Author(s):  
Huanyin Chen ◽  
Marjan Abdolyousefi
Keyword(s):  
Operator Theory ◽  
Spectral Properties ◽  
Associative Ring ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Cline’S Formula

It is well known that for an associative ring R, if ab has g-Drazin inverse then ba has g-Drazin inverse. In this case, (ba)d = b((ab)d)2a. This formula is so-called Cline?s formula for g-Drazin inverse, which plays an elementary role in matrix and operator theory. In this paper, we generalize Cline?s formula to the wider case. In particular, as applications, we obtain new common spectral properties of bounded linear operators.

Nonlocal fractional semilinear differential inclusions with noninstantaneous impulses and of order α ∈ (1, 2)

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
JinRong Wang ◽  
Ahmed G. Ibrahim ◽  
Donal O’Regan ◽  
Adel A. Elmandouh
Keyword(s):  
Differential Inclusions ◽  
Mild Solutions ◽  
Multivalued Function ◽  
Linear Operators ◽  
Solution Set ◽  
Cosine Family ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Noninstantaneous Impulses

AbstractIn this paper, we establish the existence of mild solutions for nonlocal fractional semilinear differential inclusions with noninstantaneous impulses of order α ∈ (1,2) and generated by a cosine family of bounded linear operators. Moreover, we show the compactness of the solution set. We consider both the case when the values of the multivalued function are convex and nonconvex. Examples are given to illustrate the theory.

Duality of the distance to closed operator ideals

2003 ◽  
Vol 133 (1) ◽  
pp. 197-212 ◽  
Author(s):  
Hans-Olav Tylli
Keyword(s):  
Banach Spaces ◽  
Closed Operator ◽  
Operator Ideal ◽  
Linear Operators ◽  
Distance Functions ◽  
Approximation Properties ◽  
Operator Ideals ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Special Operator

Special operator-ideal approximation properties (APs) of Banach spaces are employed to solve the problem of whether the distance functions S ↦ dist(S*, I(F*, E*)) and S ↦ dist(S, I*(E, F)) are uniformly comparable in each space L(E, F) of bounded linear operators. Here, I*(E, F) = {S ∈ L(E, F) : S* ∈ I(F*, E*)} stands for the adjoint ideal of the closed operator ideal I for Banach spaces E and F. Counterexamples are obtained for many classical surjective or injective Banach operator ideals I by solving two resulting ‘asymmetry’ problems for these operator-ideal APs.

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