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Search: All articles in the CJM digital archive with keyword linear operator

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1. CJM 2005 (vol 57 pp. 897)

Berezhnoĭ, Evgenii I.; Maligranda, Lech
Representation of Banach Ideal Spaces and Factorization of Operators
Representation theorems are proved for Banach ideal spaces with the Fatou property which are built by the Calder{\'o}n--Lozanovski\u\i\ construction. Factorization theorems for operators in spaces more general than the Lebesgue $L^{p}$ spaces are investigated. It is natural to extend the Gagliardo theorem on the Schur test and the Rubio de~Francia theorem on factorization of the Muckenhoupt $A_{p}$ weights to reflexive Orlicz spaces. However, it turns out that for the scales far from $L^{p}$-spaces this is impossible. For the concrete integral operators it is shown that factorization theorems and the Schur test in some reflexive Orlicz spaces are not valid. Representation theorems for the Calder{\'o}n--Lozanovski\u\i\ construction are involved in the proofs.

Keywords:Banach ideal spaces, weighted spaces, weight functions,, Calderón--Lozanovski\u\i\ spaces, Orlicz spaces, representation of, spaces, uniqueness problem, positive linear operators, positive sublinear, operators, Schur test, factorization of operators, f
Categories:46E30, 46B42, 46B70

2. CJM 2000 (vol 52 pp. 381)

Miyachi, Akihiko
Hardy Space Estimate for the Product of Singular Integrals
$H^p$ estimate for the multilinear operators which are finite sums of pointwise products of singular integrals and fractional integrals is given. An application to Sobolev space and some examples are also given.

Keywords:$H^p$ space, multilinear operator, singular integral, fractional integration, Sobolev space
Category:42B20

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