Results 11 to 20 of about 3,877,417 (111)
Some examples of equivalent rearrangement‐invariant quasi‐norms defined via f∗$f^*$ or f∗∗$f^{**}$
Mathematische Nachrichten, Volume 296, Issue 5, Page 1781-1802, May 2023., 2023 Abstract We consider Lorentz–Karamata spaces, small and grand Lorentz–Karamata spaces, and the so‐called L$\mathcal {L}$, R$\mathcal {R}$, LL$\mathcal {LL}$, LR$\mathcal {LR}$, RL$\mathcal {RL}$, and RR$\mathcal {RR}$ spaces. The quasi‐norms for a function f in each of these spaces can be defined via the nonincreasing rearrangement f∗$f^*$ or via the ...
Leo R. Ya. Doktorski +2 more
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On the trace embedding and its applications to evolution equations
Mathematische Nachrichten, Volume 296, Issue 4, Page 1319-1350, April 2023., 2023 Abstract In this paper, we consider traces at initial times for functions with mixed time‐space smoothness. Such results are often needed in the theory of evolution equations. Our result extends and unifies many previous results. Our main improvement is that we can allow general interpolation couples.
Antonio Agresti +2 more
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Mathematical Methods in the Applied Sciences, Volume 46, Issue 1, Page 1178-1184, 15 January 2023., 2023 In this paper, we discuss the study of some signal processing problems within Bayesian frameworks and semigroups theory, in the case where the Banach space under consideration may be nonseparable. For applications, the suggested approach may be of interest in situations where approximation in the norm of the space is not possible.
Natasha Samko, Harpal Singh
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Traces of some weighted function spaces and related non‐standard real interpolation of Besov spaces
Mathematische Nachrichten, Volume 295, Issue 9, Page 1669-1689, September 2022., 2022 Abstract We study traces of weighted Triebel–Lizorkin spaces Fp,qs(Rn,w)$F^s_{p,q}(\mathbb {R}^n,w)$ on hyperplanes Rn−k$\mathbb {R}^{n-k}$, where the weight is of Muckenhoupt type. We concentrate on the example weight wα(x)=|xn|α$w_\alpha (x) = {\big\vert x_n\big\vert }^\alpha$ when |xn|≤1$\big\vert x_n\big\vert \le 1$, x∈Rn$x\in \mathbb {R}^n$, and ...
Blanca F. Besoy +2 more
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Dyadic product BMO in the Bloom setting
Journal of the London Mathematical Society, Volume 106, Issue 2, Page 899-935, September 2022., 2022 Abstract Ó. Blasco and S. Pott showed that the supremum of operator norms over L2$L^2$ of all bicommutators (with the same symbol) of one‐parameter Haar multipliers dominates the biparameter dyadic product BMO norm of the symbol itself. In the present work we extend this result to the Bloom setting, and to any exponent 1
Spyridon Kakaroumpas +1 more
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Mathematical Methods in the Applied Sciences, Volume 45, Issue 2, Page 770-792, 30 January 2022., 2022 In this paper, we study exact boundary controllability for a linear wave equation with strong and weak interior degeneration of the coefficient in the principle part of the elliptic operator. The objective is to provide a well‐posedness analysis of the corresponding system and derive conditions for its controllability through boundary actions.
Peter I. Kogut +2 more
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A Capacity Associated with the Weighted Lebesgue Space and Its Applications
Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 In this paper, we focus on a further study of the weighted Lebesgue capacity associated with the following fractional heat equation: ∂t+−Δxαut,x=0, ∀α,t,x∈0,1×0,∞×ℝn,u0,x=fx, ∀x∈ℝn.. More properties of that capacity are explored, and applications to a trace inequality for the weak solution of the equation are considered.
Guoliang Li +3 more
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Weighted Grand Herz‐Type Spaces and Its Applications
Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 In this paper, we introduce the weighted grand Herz spaces and weighted grand Herz‐type Hardy spaces. The decompositional characterizations of these spaces are established. As its applications, the boundedness of some sublinear operators are established.
Xia Yu, Zongguang Liu, Andrea Scapellato
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Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 Let (X, d, μ) be a metric measure space endowed with a metric d and a non‐negative Borel doubling measure μ. Let L be a non‐negative self‐adjoint operator on L2(X). Assume that the (heat) kernel associated to the semigroup e−tL satisfies a Gaussian upper bound.
Jiawei Shen +3 more
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Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 In this article, we establish some new generalizations of reversed dynamic inequalities of Hilbert‐type via supermultiplicative functions by applying reverse Hölder inequalities with Specht’s ratio on time scales. We will generalize the inequalities by using a supermultiplicative function which the identity map represents a special case of it. Also, we
M. Zakarya +5 more
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