共查询到20条相似文献,搜索用时 10 毫秒
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Our aim is to introduce the grand Bochner–Lebesgue space in the spirit of Iwaniec–Sbordone spaces, also known as grand Lebesgue spaces, and prove some of its properties. We will also deal with the associate space for grand Bochner–Lebesgue spaces. 相似文献
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Archiv der Mathematik - In this paper, we show a quantitative version of the theorem stating that relatively weakly compact sets in $$\ell _1$$ coincide with those having the Banach-Saks property.... 相似文献
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In this paper, criteria for uniform nonsquareness and locally uniform nonsquareness of Orlicz–Bochner function spaces equipped with the Orlicz norm are given. Although, criteria for uniform nonsquareness and locally uniform nonsquareness in Orlicz function spaces were known, we can easily deduce them from our main results. Moreover, we give a sufficient condition for an Orlicz–Bochner function space to have the fixed point property. 相似文献
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Takashi Noiri 《Acta Mathematica Hungarica》2005,107(4):307-318
Summary New classes of sets called -closed sets and s-closed sets are introduced and studied. Also, we introduce and study -continuous functions and s-continuous functions and prove pasting lemma for these functions. Moreover, we introduce classes of topological spaces -T1/2 and -Ts. 相似文献
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M. A. Prokhorovich 《Mathematical Notes》2007,82(1-2):88-95
Let (X, μ, d) be a space of homogeneous type, where d and p are a metric and a measure, respectively, related to each other by the doubling condition with γ > 0. Let W α p (X) be generalized Sobolev classes, let Capα p (where p > 1 and 0 < α ≤ 1) be the corresponding capacity, and let dimH be the Hausdorff dimension. We show that the capacity Capα p is related to the Hausdorff dimension; we also prove that, for each function u ∈ W α/p (X), p > 1, 0 < a < γ/p, there exists a set E ? X such that dim H (E) ≤ γ - αp, the limit $$\mathop {\lim }\limits_{r \to + 0} \frac{1}{{\mu (B(x,r))}}\int_{B(x,r)} {u d\mu = u * (x)} $$ exists for each x ∈ X\E, and moreover $$\mathop {\lim }\limits_{r \to + 0} \frac{1}{{\mu (B(x,r))}}\int_{B(x,r)} {\left| {u - u * (x)} \right|^q d\mu = 0, \frac{1}{q} = \frac{1}{p} - \frac{\alpha }{\gamma }.} $$ . 相似文献
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Assume that the unit spheres of Banach spaces X and Y are uniformly homeomorphic.Then we prove that all unit spheres of the Lebesgue–Bochner function spaces L_p(μ, X) and L_q(μ, Y)are mutually uniformly homeomorphic where 1 ≤ p, q ∞. As its application, we show that if a Banach space X has Property H introduced by Kasparov and Yu, then the space L_p(μ, X), 1 ≤ p ∞,also has Property H. 相似文献
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Further investigation is done on a phenomenon studied by Zamfirescu in finite dimensions. Among other results it is proved that for most closed bounded sets A in a separable Banach space Y and most ${u \in A}$ , the union of all rays from u that meet A\{u} (resp. do not meet A\{u}) is dense in Y. An infinite-dimensional extension of a theorem of Wieacker is obtained, viz most compacta in a separable Banach space have smooth closed convex hulls. 相似文献
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M. Bonanzinga M. V. Matveev C. M. Pareek 《Rendiconti del Circolo Matematico di Palermo》2002,51(1):163-174
We prove some propositions and present some examples concerning the properties between countably compact and pseudocompact and the properties between Lindelöf and pseudo-Lindelöf. 相似文献
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Dachun Yang 《Applicable analysis》2013,92(3):549-561
In this article, the authors construct some counterexamples to show that the generalized Carleson measure space and the Triebel–Lizorkin-type space are not equivalent for certain parameters, which was claimed to be true in Lin and Wang [C.-C. Lin and K.Wang, Equivalency between the generalized Carleson measure spaces and Triebel–Lizorkin-type spaces, Taiwanese J. Math. 15 (2011), pp. 919–926]. Moreover, the authors show that for some special parameters, the generalized Carleson measure space, the Triebel–Lizorkin-type space and the Besov-type space coincide with certain Triebel–Lizorkin space, which answers a question posed in Remark 6.11(i) of Yuan et al. [W. Yuan, W. Sickel and D. Yang, Morrey and Campanato Meet Besov, Lizorkin and Triebel, Lecture Notes in Mathematics 2005, Springer-Verlag, Berlin, 2010]. In conclusion, the Triebel–Lizorkin-type space and the Besov-type space become the classical Besov spaces, when the fourth parameter is sufficiently large. 相似文献
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Surjit Singh Khurana 《Journal of Functional Analysis》2012,263(4):1098-1102
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We show the interpolation inequalities for derivatives in variable exponent Lebesgue–Sobolev spaces by applying the boundedness of the Hardy–Littlewood maximal operator on Lp(⋅). 相似文献
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Let ${s,\,\tau\in\mathbb{R}}Let
s, t ? \mathbbR{s,\,\tau\in\mathbb{R}} and q ? (0,¥]{q\in(0,\infty]} . We introduce Besov-type spaces
[(B)\dot]s, tp, q(\mathbbRn){{{{\dot B}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}}} for p ? (0, ¥]{p\in(0,\,\infty]} and Triebel–Lizorkin-type spaces
[(F)\dot]s, tp, q(\mathbbRn) for p ? (0, ¥){{{{\dot F}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}}\,{\rm for}\, p\in(0,\,\infty)} , which unify and generalize the Besov spaces, Triebel–Lizorkin spaces and Q spaces. We then establish the j{\varphi} -transform characterization of these new spaces in the sense of Frazier and Jawerth. Using the j{\varphi} -transform characterization of
[(B)\dot]s, tp, q(\mathbbRn) and [(F)\dot]s, tp, q(\mathbbRn){{{{\dot B}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}\, {\rm and}\, {{\dot F}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}}} , we obtain their embedding and lifting properties; moreover, for appropriate τ, we also establish the smooth atomic and
molecular decomposition characterizations of
[(B)\dot]s, tp, q(\mathbbRn) and [(F)\dot]s, tp, q(\mathbbRn){{{{\dot B}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}\,{\rm and}\, {{\dot F}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}}} . For
s ? \mathbbR{s\in\mathbb{R}} , p ? (1, ¥), q ? [1, ¥){p\in(1,\,\infty), q\in[1,\,\infty)} and
t ? [0, \frac1(max{p, q})¢]{\tau\in[0,\,\frac{1}{(\max\{p,\,q\})'}]} , via the Hausdorff capacity, we introduce certain Hardy–Hausdorff spaces
B[(H)\dot]s, tp, q(\mathbbRn){{{{B\dot{H}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}}}} and prove that the dual space of
B[(H)\dot]s, tp, q(\mathbbRn){{{{B\dot{H}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}}}} is just
[(B)\dot]-s, tp¢, q¢(\mathbbRn){\dot{B}^{-s,\,\tau}_{p',\,q'}(\mathbb{R}^{n})} , where t′ denotes the conjugate index of t ? (1,¥){t\in (1,\infty)} . 相似文献