| 1. |
- Aalto, Daniel, et al.
(author)
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John-Nirenberg lemmas for a doubling measure
- 2011
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In: Studia Mathematica. - : Institute of Mathematics, Polish Academy of Sciences. - 0039-3223 .- 1730-6337. ; 204:1, s. 21-37
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Journal article (peer-reviewed)abstract
- We study, in the context of doubling metric measure spaces, a class of BMO type functions defined by John and Nirenberg. In particular, we present a new version of the Calderon-Zygmund decomposition in metric spaces and use it to prove the corresponding John Nirenberg inequality.
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| 2. |
- Alaghmandan, Mahmood, 1983, et al.
(author)
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Fourier algebras of hypergroups and central algebras on compact (quantum) groups
- 2017
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In: Studia Mathematica. - : Institute of Mathematics, Polish Academy of Sciences. - 0039-3223 .- 1730-6337. ; 239:3, s. 225-247
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Journal article (peer-reviewed)abstract
- © Instytut Matematyczny PAN, 2017. This paper concerns the study of regular Fourier hyper groups through multipliers of their associated Fourier algebras. We establish hypergroup analogues of well-known characterizations of group amenability, introduce a notion of weak amenability for hypergroups, and show that every discrete commutative hypergroup is weakly amenable with constant 1. Using similar techniques, we provide a sufficient condition for amenability of hypergroup Fourier algebras, which, as an immediate application, answers one direction of a conjecture of Azimifard-Samei-Spronk (2009) on the amenability of ZL 1 (G) for compact groups G. In the final section we consider Fourier algebras of hypergroups arising from compact quantum groups G, and in particular establish a completely isometric isomorphism with the center of the quantum group algebra for compact G of Kac type.
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| 3. |
- Aleman, Alexandru, et al.
(author)
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An Hp scale for complete Pick spaces
- 2021
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In: Studia Mathematica. - 0039-3223. ; 258:3, s. 343-359
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Journal article (peer-reviewed)abstract
- We define by interpolation a scale analogous to the Hardy Hp scale for complete Pick spaces, and establish some of the basic properties of the resulting spaces, which we call Hp. In particular, we obtain an Hp-Hq duality and establish sharp pointwise estimates for functions in Hp
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| 4. |
- Aleman, Alexandru, et al.
(author)
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Uniform spectral radius and compact Gelfand transform
- 2006
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In: Studia Mathematica. - 0039-3223. ; 172:1, s. 25-46
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Journal article (peer-reviewed)abstract
- We consider the quantization of inversion in commutative p-normed quasi-Banach algebras with unit. The standard questions considered for such an algebra A with unit e and Gelfand transform x bar right arrow (x) over cap are: (i) Is K-nu = sup{parallel to(e - x)(-1)parallel to(p) : x is an element of A, parallel to x parallel to(p) <= 1, max (x) over cap <= nu} bounded, where nu is an element of (0, 1)? (ii) For which delta is an element of (0, 1) is C-delta = sup{parallel to x(-1)parallel to(p) : x is an element of A, parallel to x parallel to(p) <= 1, min (x) over cap >= delta} bounded? Both questions are related to a "uniform spectral radius" of the algebra, r(infinity)(A), introduced by Bjork. Question (i) has an affirmative answer if and only if r(infinity)(A) < 1, and this result is extended to more general nonlinear extremal problems of this type. Question (ii) is more difficult, but it can also be related to the uniform spectral radius. For algebras with compact Gelfand transform we prove that the answer is "yes" for all delta is an element of (0, 1) if and only if r(infinity)(A) = 0. Finally, we specialize to semisimple Beurling type algebras l(w)(p)(D), where 0 < p < 1 and D = N or D = Z. We show that the number r(infinity)(l(w)(p)(D)) can be effectively computed in terms of the underlying weight. In particular, this solves questions (i) and (ii) for many of these algebras. We also construct weights such that the corresponding Beurling algebra has a compact Gelfand transform, but the uniform spectral radius equals an arbitrary given number in (0, 1].
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| 5. |
- Asekritova, Irina, et al.
(author)
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Distribution and Rearranement Estimates of the Maximal Functions and Interpolation
- 1997
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In: Studia Mathematica. - 0039-3223 .- 1730-6337. ; 124:2, s. 107-132
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Journal article (peer-reviewed)abstract
- There are given necessary and sufficient conditions on a measure dμ(x)=w(x)dx under which the key estimates for the distribution and rearrangement of the maximal function due to Riesz, Wiener, Herz and Stein are valid. As a consequence, we obtain the equivalence of the Riesz and Wiener inequalities which seems to be new even for the Lebesgue measure. Our main tools are estimates of the distribution of the averaging function f** and a modified version of the Calderón-Zygmund decomposition. Analogous methods allow us to obtain K-functional formulas in terms of the maximal function for couples of weighted $L_p$-spaces.
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| 6. |
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| 7. |
- Asekritova, Irina, et al.
(author)
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Lions-Peetre Reiteration Formulas for Triples and Their Application
- 2001
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In: Studia Mathematica. - : Institute of Mathematics, Polish Academy of Sciences. - 0039-3223 .- 1730-6337. ; 145:3, s. 219-254
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Journal article (peer-reviewed)abstract
- We present, discuss and apply two reiteration theorems for triples of quasi-Banach function lattices. Some interpolation results for block-Lorentz spaces and triples of weighted Lp-spaces are proved. By using these results and a wavelet theory approach we calculate (θ,q)-spaces for triples of smooth function spaces (such as Besov spaces, Sobolev spaces, etc.). In contrast to the case of couples, for which even the scale of Besov spaces is not stable under interpolation, for triples we obtain stability in the frame of Besov spaces based on Lorentz spaces. Moreover, by using the results and ideas of this paper, we can extend the Stein–Weiss interpolation theorem known for Lp(μ)-spaces with change of measures to Lorentz spaces with change of measures. In particular, the results obtained show that for some problems in analysis the three-space real interpolation approach is really more useful than the usual real interpolation between couples.
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| 8. |
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| 9. |
- Asekritova, Irina, et al.
(author)
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Lizorkin-Freitag Formula for Several Weighted Lp Spaces and Vector-Valued Interpolation
- 2005
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In: Studia Mathematica. - : Institute of Mathematics, Polish Academy of Sciences. - 0039-3223 .- 1730-6337. ; 170:3, s. 227-239
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Journal article (peer-reviewed)abstract
- A complete description of the real interpolation space L=(Lp0(ω0),…,Lpn(ωn))θ⃗ ,q is given. An interesting feature of the result is that the whole measure space (Ω,μ) can be divided into disjoint pieces Ωi (i∈I) such that L is an lq sum of the restrictions of L to Ωi, and L on each Ωi is a result of interpolation of just two weighted Lp spaces. The proof is based on a generalization of some recent results of the first two authors concerning real interpolation of vector-valued spaces.
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| 10. |
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