共查询到20条相似文献,搜索用时 31 毫秒
1.
Feng Dai 《Journal of Mathematical Analysis and Applications》2006,315(2):711-724
We study the Kolmogorov m-widths and the linear m-widths of the weighted Besov classes on [−1,1], where Lq,μ, 1?q?∞, denotes the Lq space on [−1,1] with respect to the measure , μ>0. Optimal asymptotic orders of and as m→∞ are obtained for all 1?p,τ?∞. It turns out that in many cases, the orders of are significantly smaller than the corresponding orders of the best m-term approximation by ultraspherical polynomials, which is somewhat surprising. 相似文献
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Hua Wang 《Journal of Mathematical Analysis and Applications》2011,381(1):134-145
In this paper, by using the atomic decomposition and molecular characterization of the homogeneous and non-homogeneous weighted Herz-type Hardy spaces , we obtain some weighted boundedness properties of the Bochner-Riesz operator and the maximal Bochner-Riesz operator on these spaces for α=n(1/p−1/q), 0<p?1 and 1<q<∞. 相似文献
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Sergej N. Melikhov 《Journal of Mathematical Analysis and Applications》2004,297(2):577-586
Let be a bounded convex domain, A−∞(G) be the (DFS)-space of all holomorphic functions of polynomial growth on G and A∞(G) be the Fréchet space of C∞-functions on closure of G which are holomorphic on G. With the help of the Laplace transform we describe the strong dual of A−∞(G) and prove that A−∞(G) is the unique (DFS)-space H such that the space A∞(G) is contained in H, H is embedded continuously in A−∞(G) and H is invariant under differentiation. 相似文献
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Joaquín Motos María Jesús Planells César F. Talavera 《Journal of Mathematical Analysis and Applications》2008,338(1):162-174
It is proved that the Hörmander and spaces (Ω1⊂Rn, Ω2⊂Rm open sets, 1?p<∞, ki Beurling-Björck weights, k=k1⊗k2) are isomorphic whereas the iterated spaces and are not if 1<p≠q<∞. A similar result for weighted Lp-spaces of entire analytic functions is also obtained. Finally a result on iterated Besov spaces is given: and are not isomorphic when 1<q≠2<∞. 相似文献
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Alexei Yu. Karlovich Ilya M. Spitkovsky 《Journal of Mathematical Analysis and Applications》2011,384(2):706-725
Let a be a semi-almost periodic matrix function with the almost periodic representatives al and ar at −∞ and +∞, respectively. Suppose p:R→(1,∞) is a slowly oscillating exponent such that the Cauchy singular integral operator S is bounded on the variable Lebesgue space Lp(⋅)(R). We prove that if the operator aP+Q with P=(I+S)/2 and Q=(I−S)/2 is Fredholm on the variable Lebesgue space , then the operators alP+Q and arP+Q are invertible on standard Lebesgue spaces and with some exponents ql and qr lying in the segments between the lower and the upper limits of p at −∞ and +∞, respectively. 相似文献
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Mahamadi Warma 《Journal of Mathematical Analysis and Applications》2007,336(2):1132-1148
Let Ω⊂RN be a bounded domain with Lipschitz boundary, with a>0 on . Let σ be the restriction to ∂Ω of the (N−1)-dimensional Hausdorff measure and let be σ-measurable in the first variable and assume that for σ-a.e. x∈∂Ω, B(x,⋅) is a proper, convex, lower semicontinuous functional. We prove in the first part that for every p∈(1,∞), the operator Ap:=div(a|∇u|p−2∇u) with nonlinear Wentzell-Robin type boundary conditions
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Antonio S. Granero 《Journal of Mathematical Analysis and Applications》2007,326(2):1383-1393
If X is a Banach space and C⊂X∗∗ a convex subset, for x∗∗∈X∗∗ and A⊂X∗∗ let be the distance from x∗∗ to C and . In this paper we prove that if φ is an Orlicz function, I an infinite set and X=?φ(I) the corresponding Orlicz space, equipped with either the Luxemburg or the Orlicz norm, then for every w∗-compact subset K⊂X∗∗ we have if and only if φ satisfies the Δ2-condition at 0. We also prove that for every Banach space X, every nonempty convex subset C⊂X and every w∗-compact subset K⊂X∗∗ then and, if K∩C is w∗-dense in K, then . 相似文献
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Vagif S. Guliyev Yagub Y. Mammadov 《Journal of Mathematical Analysis and Applications》2009,353(1):449-459
In this paper we obtain necessary and sufficient conditions on the parameters for the boundedness of the Dunkl-type fractional maximal operator Mβ, and the Dunkl-type fractional integral operator Iβ from the spaces Lp,α(R) to the spaces Lq,α(R), 1<p<q<∞, and from the spaces L1,α(R) to the weak spaces WLq,α(R), 1<q<∞. In the case , we prove that the operator Mβ is bounded from the space Lp,α(R) to the space L∞,α(R), and the Dunkl-type modified fractional integral operator is bounded from the space Lp,α(R) to the Dunkl-type BMO space BMOα(R). By this results we get boundedness of the operators Mβ and Iβ from the Dunkl-type Besov spaces to the spaces , 1<p<q<∞, 1/p−1/q=β/(2α+2), 1?θ?∞ and 0<s<1. 相似文献
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A. Ben Dkhil 《Journal of Mathematical Analysis and Applications》2010,371(1):363-371
We prove some existence results of positive continuous solutions to the semilinear parabolic system , in an unbounded domain D with compact boundary subject to some Dirichlet conditions, where λ and μ are nonnegative parameters. The functions f, g are nonnegative continuous monotone on (0,∞) and the potentials p, q are nonnegative and satisfy some hypotheses related to the parabolic Kato class J∞(D). 相似文献
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Seppo Hassi 《Journal of Mathematical Analysis and Applications》2003,282(2):584-602
Assume that the differential operator −DpD+q in L2(0,∞) has 0 as a regular point and that the limit-point case prevails at ∞. If p≡1 and q satisfies some smoothness conditions, it was proved by Gelfand and Levitan that the spectral functions σ(t) for the Sturm-Liouville operator corresponding to the boundary conditions (pu′)(0)=τu(0), , satisfy the integrability condition . The boundary condition u(0)=0 is exceptional, since the corresponding spectral function does not satisfy such an integrability condition. In fact, this situation gives an example of a differential operator for which one can construct an analog of the Friedrichs extension, even though the underlying minimal operator is not semibounded. In the present paper it is shown with simple arguments and under mild conditions on the coefficients p and q, including the case p≡1, that there exists an analog of the Friedrichs extension for nonsemibounded second order differential operators of the form −DpD+q by establishing the above mentioned integrability conditions for the underlying spectral functions. 相似文献
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We prove the boundedness of Calderón-Zygmund operators on weighted amalgam spaces for 1<p,q<∞ with Muckenhoupt weights. To do this, we show the boundedness in the discrete case, i.e. the boundedness on . We also investigate on . As an application we consider an operator related to the Navier-Stokes equation. 相似文献
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C.L. Prather 《Journal of Mathematical Analysis and Applications》2009,349(1):55-67
Let L=(1−x2)D2−((β−α)−(α+β+2)x)D with , and . Let f∈C∞[−1,1], , with normalized Jacobi polynomials and the Cn decrease sufficiently fast. Set Lk=L(Lk−1), k?2. Let ρ>1. If the number of sign changes of (Lkf)(x) in (−1,1) is O(k1/(ρ+1)), then f extends to be an entire function of logarithmic order . For Legendre expansions, the result holds with replaced with . 相似文献
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Chris Lennard 《Journal of Mathematical Analysis and Applications》2009,350(1):384-392
We study certain Hardy-type sequence spaces Hp and , 1?p?∞, which are analogues of ?∞ and c0, respectively. We show that the Mazur product is not onto for every p∈(1,∞) with q=p−1(p−1). We present corollaries for spaces defined via weighted ?p seminorms and for c0. The latter corollary provides a new solution of Mazur's Problem 8 in the Scottish Book. 相似文献
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Ming-Yi Lee 《Journal of Mathematical Analysis and Applications》2006,324(2):1274-1281
Let w be a Muckenhoupt weight and be the weighted Hardy spaces. We use the atomic decomposition of and their molecular characters to show that the Bochner-Riesz means are bounded on for 0<p?1 and δ>max{n/p−(n+1)/2,[n/p]rw−1(rw−1)−(n+1)/2}, where rw is the critical index of w for the reverse Hölder condition. We also prove the boundedness of the maximal Bochner-Riesz means for 0<p?1 and δ>n/p−(n+1)/2. 相似文献
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Erd?s, Horváth and Joó discovered some years ago that for some real numbers 1<q<2 there exists only one sequence ci of zeroes and ones such that ∑ciq−i=1. Subsequently, the set U of these numbers was characterized algebraically in [P. Erd?s, I. Joó, V. Komornik, Characterization of the unique expansions 1=∑q−ni and related problems, Bull. Soc. Math. France 118 (1990) 377-390] and [V. Komornik, P. Loreti, Subexpansions, superexpansions and uniqueness properties in non-integer bases, Period. Math. Hungar. 44 (2) (2002) 195-216]. We establish an analogous characterization of the closure of U. This allows us to clarify the topological structure of these sets: is a countable dense set of , so the latter set is perfect. Moreover, since U is known to have zero Lebesgue measure, is a Cantor set. 相似文献
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So-Chin Chen 《Journal of Mathematical Analysis and Applications》2004,297(1):38-47
In contrast to the famous Henkin-Skoda theorem concerning the zero varieties of holomorphic functions in the Nevanlinna class on the open unit ball Bn in , n?2, it is proved in this article that for any nonnegative, increasing, convex function ?(t) defined on , there exists satisfying such that there is no f∈Hp(Bn), 0<p<∞, with . Here Ng(ζ,1) denotes the integrated zero counting function associated with the slice function gζ. This means that the zero sets of holomorphic functions belonging to the Hardy spaces Hp(Bn), 0<p<∞, unlike that of the holomorphic functions in the Nevanlinna class, cannot be characterized in the above manner. 相似文献