Multipliers on D α

Taylor, G. D.

doi:10.2307/1994621

Cited by 23 publications

(18 citation statements)

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“…Taylor [36], for the one dimensional case, and D. Jupiter and D. Redett [21], for the multidimensional case, the Dirichlet type space D α is defined as the space of all functions f ∈ H(D N ) with representation (2.5) subject to the condition (2.6)…”

Section: Weighted Sobolev Spacesmentioning

confidence: 99%

Triplets of Closely Embedded Hilbert Spaces

Cojuhari

Gheondea

2014

Integr. Equ. Oper. Theory

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Abstract. We obtain a general concept of triplet of Hilbert spaces with closed (unbounded) embeddings instead of continuous (bounded) ones. We provide a model and an abstract theorem as well for a triplet of closely embedded Hilbert spaces associated to positive selfadjoint operator H, that is called the Hamiltonian of the system, which is supposed to be one-to-one but may not have a bounded inverse. Existence and uniqueness results, as well as left-right symmetry, for these triplets of closely embedded Hilbert spaces are obtained. We motivate this abstract theory by a diversity of problems coming from homogeneous or weighted Sobolev spaces, Hilbert spaces of holomorphic functions, and weighted L 2 spaces. An application to weak solutions for a Dirichlet problem associated to a class of degenerate elliptic partial differential equations is presented. In this way, we propose a general method of proving the existence of weak solutions that avoids coercivity conditions and Poincaré-Sobolev type inequalities.

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Section: Weighted Sobolev Spacesmentioning

confidence: 99%

Triplets of Closely Embedded Hilbert Spaces

Cojuhari

Gheondea

2014

Integr. Equ. Oper. Theory

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“…Let α ∈ R N be fixed. Following Taylor [24], for the one dimensional case, and Jupiter and Redett [16], for the multidimensional case, the Dirichlet type space D α consists, by definition, on all functions f ∈ H (D N ) with representation (3.1) subject to the condition…”

Section: Triplets Of Dirichlet Type Spaces: the General Casementioning

confidence: 99%

“…The class of Dirichlet type spaces, see Sect. 3 for definition, has been introduced and studied in connection to multipliers' theory by Taylor [24], for the one dimensional case, and by Jupiter and Redett [16], for the multidimensional case. In this respect we note that the notion of "H 2 duality", that is well-known in the theory of spaces of analytic functions, is close to the notion of triplet of Hilbert spaces when the middle space is the Hardy space H 2 , e.g.…”

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confidence: 99%

Triplets of Closely Embedded Dirichlet Type Spaces on the Unit Polydisc

Cojuhari

Gheondea

2012

Complex Anal. Oper. Theory

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We propose a general concept of triplet of Hilbert spaces with closed embeddings, instead of continuous ones, and we show how rather general weighted L 2 spaces yield this kind of generalized triplets of Hilbert spaces for which the underlying spaces and operators can be explicitly calculated. Then we show that generalized triplets of Hilbert spaces with closed embeddings can be naturally associated to any pair of Dirichlet type spaces D α (D N ) of holomorphic functions on the unit polydisc D N and we explicitly calculate the associated operators in terms of reproducing kernels and radial derivative operators. We also point out a rigging of the Hardy space H 2 (D N ) through a scale of Dirichlet type spaces and Bergman type spaces.Keywords Closed embedding · Triplet of Hilbert spaces · Rigged Hilbert spaces · Dirichlet type space on the unit polydisc · Kernel operator · Hamiltonian

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“…D n is the Dirichlet space. In the setting of disk, the Dirichlet type space D p was defined by Taylor (see [12]). Dirichlet type space was studied in many different aspects, such as integral characterizations, multipliers and Carleson measure (see [5,8,10,12]).…”

Section: Introductionmentioning

confidence: 99%

Some new characterizations of Dirichlet type spaces on the unit ball of Cn

2006

Journal of Mathematical Analysis and Applications

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Multipliers on D α

Cited by 23 publications

References 0 publications

Triplets of Closely Embedded Hilbert Spaces

Triplets of Closely Embedded Hilbert Spaces

Triplets of Closely Embedded Dirichlet Type Spaces on the Unit Polydisc

Some new characterizations of Dirichlet type spaces on the unit ball of Cn

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