On the Riesz Almost Convergent Sequences Space
The purpose of this paper is to introduce new spaces 𝑓 and 𝑓0 that consist of all sequences whose Riesz transforms of order one are in the spaces 𝑓 and 𝑓0, respectively. We also show that 𝑓 and 𝑓0 are linearly isomorphic to the spaces 𝑓 and 𝑓0, respectively. The 𝛽- and 𝛾-duals of the spaces 𝑓 a...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/691694 |
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| Summary: | The purpose of this paper is to introduce new spaces 𝑓 and 𝑓0 that consist of all sequences whose Riesz transforms of order one are in the spaces 𝑓 and 𝑓0, respectively. We also show that 𝑓 and 𝑓0 are linearly isomorphic to the spaces 𝑓 and 𝑓0, respectively. The 𝛽- and 𝛾-duals of the spaces 𝑓 and 𝑓0 are computed. Furthermore, the classes (𝑓∶𝜇) and (𝜇∶𝑓) of infinite matrices are characterized for any given sequence space 𝜇 and determine the necessary and sufficient conditions on a matrix 𝐴 to satisfy 𝐵𝑅−core(𝐴𝑥)⊆𝐾−core(𝑥), 𝐵𝑅−core(𝐴𝑥)⊆𝑠𝑡−core(𝑥) for all 𝑥∈ℓ∞. |
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| ISSN: | 1085-3375 1687-0409 |