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1.
Conditions on weightsu(·),v(·) are given so that a classical operatorT sends the weighted Lorentz spaceL Lrs (vdx) intoL pq (udx). HereT is either a fractional maximal operatorM α or a fractional integral operatorI α or a Calderón-Zygmund operator. A characterization of this boundedness is obtained forM α andI α when the weights have some usual properties and max(r, s) ≤ min(p, q).  相似文献   

2.
The generalized maximal operator M in martingale spaces is considered. For 1 < pq < ∞, the authors give a necessary and sufficient condition on the pair ([^(m)]\hat \mu , v) for M to be a bounded operator from martingale space L p (v) into L q ([^(m)]\hat \mu ) or weak-L q ([^(m)]\hat \mu ), where [^(m)]\hat \mu is a measure on Ω × ℕ and v a weight on Ω. Moreover, the similar inequalities for usual maximal operator are discussed.  相似文献   

3.
This paper deals with the strongly coupled parabolic system ut = v^m△u, vt = u^n△v, (x, t) ∈Ω × (0,T) subject to nonlinear boundary conditions 偏du/偏dη = u^αv^p, 偏du/偏dη= u^qv^β, (x, t) ∈ 偏dΩ × (0, T), where Ω 包含 RN is a bounded domain, m, n are positive constants and α,β, p, q are nonnegative constants. Global existence and nonexistence of the positive solution of the above problem are studied and a new criterion is established. It is proved that the positive solution of the above problem exists globally if and only if α 〈 1,β 〈 1 and (m +p)(n + q) ≤ (1 - α)(1 -β).  相似文献   

4.
LetT Ω,α (0 ≤ α< n) be the singular and fractional integrals with variable kernel Ω(x, z), and [b, TΩ,α] be the commutator generated by TΩ,α and a Lipschitz functionb. In this paper, the authors study the boundedness of [b, TΩ,α] on the Hardy spaces, under some assumptions such as theL r -Dini condition. Similar results and the weak type estimates at the end-point cases are also given for the homogeneous convolution operators . The smoothness conditions imposed on are weaker than the corresponding known results.  相似文献   

5.
In the present paper we consider a von Neumann algebra M with a faithful normal semi-finite trace τ, and {α t }, a strongly continuous extension to L p (M, τ) of a semigroup of absolute contractions on L 1(M, τ). By means of a non-commutative Banach Principle we prove for a Besicovitch function b and xL p (M, τ), that the averages 1/T0 T b(t)α t (x)dt converge bilateral almost uniformly in L p (M, τ) as T → 0. Communicated by Dénes Petz  相似文献   

6.
Let Ω be an open and bounded subset ofR n with locally Lipschitz boundary. We prove that the functionsv∈SBV(Ω,R m ) whose jump setS vis essentially closed and polyhedral and which are of classW k, ∞ (S v,R m) for every integerk are strongly dense inGSBV p(Ω,R m ), in the sense that every functionu inGSBV p(Ω,R m ) is approximated inL p(Ω,R m ) by a sequence of functions {v k{j∈N with the described regularity such that the approximate gradients ∇v jconverge inL p(Ω,R nm ) to the approximate gradient ∇u and the (n−1)-dimensional measure of the jump setsS v j converges to the (n−1)-dimensional measure ofS u. The structure ofS v can be further improved in casep≤2.
Sunto Sia Ω un aperto limitato diR n con frontiera localmente Lipschitziana. In questo lavoro si dimostra che le funzioniv∈SBV(Ω,R m ) con insieme di saltoS v essenzialmente chiuso e poliedrale che sono di classeW k, ∞ (S v,R m ) per ogni interok sono fortemente dense inGSBV p(Ω,R m ), nel senso che ogni funzioneuGSBV p(Ω,R m ) è approssimata inL p(Ω,R m ) da una successione di funzioni {v j}j∈N con la regolaritá descritta tali che i gradienti approssimati ∇v jconvergono inL p(Ω,R nm ) al gradiente approssimato ∇u e la misura (n−1)-dimensionale degli insiemi di saltoS v jconverge alla misura (n−1)-dimensionale diS u. La struttura diS vpuó essere migliorata nel caso in cuip≤2.
  相似文献   

7.
Given a fixed probability space (Ω,ℱ,ℙ) and m≥1, let X(t) be an L2(Ω) process satisfying necessary regularity conditions for existence of the mth iterated stochastic integral. For real-valued processes, these existence conditions are known from the work of D. Engel. Engel’s work is extended here to L2(Ω) processes defined on Clifford algebras of arbitrary signature (p,q), which reduce to the real case when p=q=0. These include as special cases processes on the complex numbers, quaternion algebra, finite fermion algebras, fermion Fock spaces, space-time algebra, the algebra of physical space, and the hypercube. Next, a graph-theoretic approach to stochastic integrals is developed in which the mth iterated stochastic integral corresponds to the limit in mean of a collection of weighted closed m-step walks on a growing sequence of graphs. Combinatorial properties of the Clifford geometric product are then used to create adjacency matrices for these graphs in which the appropriate weighted walks are recovered naturally from traces of matrix powers. Given real-valued L2(Ω) processes, Hermite and Poisson-Charlier polynomials are recovered in this manner.  相似文献   

8.
The two-dimensional classical Hardy space Hp(T×T) on the bidisc are introduced, and it is shown that the maximal operator of the (C,α,β) means of a distribution is bounded from the space Hp(T×T) to Lp(T2) (1/(α+1), 1/(β+1)<p≤∞), and is of weak type (H 1 # (T×T), L1(T2)), where the Hardy space H 1 # (T×T) is defined by the hybrid maximal function. As a consequence we obtain that the (C, α, β) means of a function f∈H 1 # (T×T)⊃LlogL(T 2) convergs a. e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on the spaces Hp(T×T) whenever 1/(α+1), 1(β+1)<p<∞. Thus, in case f∈Hp(T×T), the (C, α, β) means convergs to f in Hp(T×T) norm whenever (1/(α+1), 1/(β+1)<p<∞). The same results are proved for the conjugate (C, α, β) means, too. This research was made while the author was visiting the Humboldt University in Berlin supported by the Alexander von Humboldt Foundation.  相似文献   

9.
The two-dimensional classical Hardy space Hp(T×T) on the bidisc are introduced, and it is shown that the maximal operator of the (C,α,β) means of a distribution is bounded from the space Hp(T×T) to Lp(T2) (1/(α+1), 1/(β+1)<p≤∞), and is of weak type (H 1 # (T×T), L1(T2)), where the Hardy space H 1 # (T×T) is defined by the hybrid maximal function. As a consequence we obtain that the (C, α, β) means of a function f∈H 1 # (T×T)⊃LlogL(T 2) convergs a. e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on the spaces Hp(T×T) whenever 1/(α+1), 1(β+1)<p<∞. Thus, in case f∈Hp(T×T), the (C, α, β) means convergs to f in Hp(T×T) norm whenever (1/(α+1), 1/(β+1)<p<∞). The same results are proved for the conjugate (C, α, β) means, too.  相似文献   

10.
In this paper, we prove the commutator T b generated by the strongly singular integral operator T and the function b is bounded from L p (w) to L q (w 1−q ) if and only if bLip β (w), where wA 1, 0 < β < 1, 1 < p < n/β and 1/q = 1/pβ/n. To do this, we first show a maximal function estimate for the commutator.  相似文献   

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