603 research outputs found
Weighted Calderón-Hardy spaces
No full textsummary:We present the weighted Calderón-Hardy spaces on Euclidean spaces and investigate their properties. As an application we show, for certain power weights, that the iterated Laplace operator is a bijection from these spaces onto classical weighted Hardy spaces. The main tools to achieve our result are an atomic decomposition of weighted Hardy spaces furnished by the author, fundamental solutions of iterated Laplacian and pointwise inequalities for certain maximal functions
Isomorphisms and several characterizations of Musielak-Orlicz-Hardy spaces associated with some Schrödinger operators
No full textsummary:Let be a Schrödinger operator on with and satisfying . Assume that is a function such that is an Orlicz function, (the class of uniformly Muckenhoupt weights). Let be an -harmonic function on with , where and are positive constants. In this article, the author proves that the mapping is an isomorphism from the Musielak-Orlicz-Hardy space associated with , , to the Musielak-Orlicz-Hardy space under some assumptions on . As applications, the author further obtains the atomic and molecular characterizations of the space associated with , and proves that the operator is an isomorphism of the spaces and . All these results are new even when , for all and , with and some
More on the density of analytic polynomials in abstract Hardy spaces
No full textLet be the sequence of the Fej\'er kernels on the unit circle . The first author recently proved that if is a separable Banach function space on such that the Hardy-Littlewood maximaloperator is bounded on its associate space , then for every as . This implies that the set of analyticpolynomials is dense in the abstract Hardy space built upon a separable Banach function space such that is bounded on . In this note we show that there exists a separable weighted space such that the sequence does not always converge to in the norm of . On the other hand, we prove that the set is dense in under the assumption that is merely separable.<br/
Existence of solutions for quasilinear elliptic equations with Hardy potential
No full textIn this paper, we consider the following quasilinear elliptic equation with Hardy potential and Dirichlet boundary condition: -Sigma(N)(i,j=1) D-j(a(i j)(x, u)D(i)u) + 1/2 Sigma(N)(i,j=1) D(s)a(i,j)(x, u)D(i)uD(j)u - lambda|x|(-2)u = f (x, u) in Omega, where Omega subset of R-N (N >= 3) is a smooth bounded domain, D-i = partial derivative/partial derivative x(i), D(s)a(i j)(x, s) = partial derivative/partial derivative s a(i j)(x, s), and 0 <= lambda < lambda* := (N-2/2)(2), and lambda|x|(-2) is called the Hardy potential. By using the perturbation method, we prove the existence of infinitely many solutions for the above problem. (C) 2016 AIP Publishing LLC.NSFC [11151040, 11331010, 11371160, 11271331]SCI(E)[email protected]; [email protected]; [email protected]
Open access self-archiving: An author study
No full textThis, our second author international, cross-disciplinary study on open access had 1296 respondents. Its focus was on self-archiving. Almost half (49%) of the respondent population have self-archived at least one article during the last three years. Use of institutional repositories for this purpose has doubled and usage has increased by almost 60% for subject-based repositories. Self-archiving activity is greatest amongst those who publish the largest number of papers. There is still a substantial proportion of authors unaware of the possibility of providing open access to their work by self-archiving. Of the authors who have not yet self-archived any articles, 71% remain unaware of the option. With 49% of the author population having self-archived in some way, this means that 36% of the total author population (71% of the remaining 51%), has not yet been appraised of this way of providing open access. Authors have frequently expressed reluctance to self-archive because of the perceived time required and possible technical difficulties in carrying out this activity, yet findings here show that only 20% of authors found some degree of difficulty with the first act of depositing an article in a repository, and that this dropped to 9% for subsequent deposits. Another author worry is about infringing agreed copyright agreements with publishers, yet only 10% of authors currently know of the SHERPA/RoMEO list of publisher permissions policies with respect to self-archiving, where clear guidance as to what a publisher permits is provided. Where it is not known if permission is required, however, authors are not seeking it and are self-archiving without it. Communicating their results to peers remains the primary reason for scholars publishing their work; in other words,
researchers publish to have an impact on their field. The vast majority of authors (81%) would willingly comply with a mandate from their employer or research funder to deposit copies of their articles in an institutional or subject-based repository. A further 13% would comply reluctantly; 5% would not comply with such a mandate
The Hardy class of a Bazilevič function and its derivative
No full textThe Bazilevič function
f
(
z
)
f(z)
defined in
Δ
:
|
z
|
>
1
\Delta :|z| > 1
by
f
(
z
)
≡
[
α
∫
0
z
P
(
ζ
)
g
(
ζ
)
α
ζ
−
1
d
ζ
]
1
/
α
f(z) \equiv {[\alpha \smallint _0^zP(\zeta )g{(\zeta )^\alpha }{\zeta ^{ - 1}}d\zeta ]^{1/\alpha }}
where
g
(
ζ
)
g(\zeta )
is starlike in
Δ
\Delta
,
P
(
ζ
)
P(\zeta )
is regular with Re
P
(
ζ
)
>
0
P(\zeta ) > 0
in
Δ
\Delta
and
α
>
0
\alpha > 0
is univalent. The class of such functions contains many of the special classes of univalent functions. The author determines the Hardy classes to which
f
(
z
)
f(z)
and
f
′
(
z
)
f’(z)
belong. In addition if
f
(
z
)
=
∑
0
∞
a
n
z
n
f(z) = \sum \nolimits _0^\infty {{a_n}{z^n}}
the limiting value of
|
a
n
|
/
n
|{a_n}|/n
is obtained.</p
Resultados de existência para equações elípticas com termos singulares
No full textDoutoramento em Matemática e AplicaçõesEsta dissertação estuda em detalhe três problemas elípticos: (I) uma classe de
equações que envolve o operador Laplaciano, um termo singular e nãolinearidade
com o exponente crítico de Sobolev, (II) uma classe de equações
com singularidade dupla, o expoente crítico de Hardy-Sobolev e um termo
côncavo e (III) uma classe de equações em forma divergente, que envolve um
termo singular, um operador do tipo Leray-Lions, e uma função definida nos
espaços de Lorentz.
As não-linearidades consideradas nos problemas (I) e (II), apresentam
dificuldades adicionais, tais como uma singularidade forte no ponto zero (de
modo que um "blow-up" pode ocorrer) e a falta de compacidade, devido à
presença do exponente crítico de Sobolev (problema (I)) e Hardy-Sobolev
(problema (II)). Pela singularidade existente no problema (III), a definição
padrão de solução fraca pode não fazer sentido, por isso, é introduzida uma
noção especial de solução fraca em subconjuntos abertos do domínio.
Métodos variacionais e técnicas da Teoria de Pontos Críticos são usados para
provar a existência de soluções nos dois primeiros problemas. No problema (I),
são usadas uma combinação adequada de técnicas de Nehari, o princípio
variacional de Ekeland, métodos de minimax, um argumento de translação e
estimativas integrais do nível de energia. Neste caso, demonstramos a
existência de (pelo menos) quatro soluções não triviais onde pelo menos uma
delas muda de sinal. No problema (II), usando o método de concentração de
compacidade e o teorema de passagem de montanha, demostramos a
existência de pelo menos duas soluções positivas e pelo menos um par de
soluções com mudança de sinal. A abordagem do problema (III) combina um
resultado de surjectividade para operadores monótonos, coercivos e
radialmente contínuos com propriedades especiais do operador de tipo Leray-
Lions. Demonstramos assim a existência de pelo menos, uma solução no
espaço de Lorentz e obtemos uma estimativa para esta solução.This dissertation study mainly three elliptical problems: (I) a class of equations,
which involves the Laplacian operator, a singular term and a nonlinearity with
the critical Sobolev exponent, (II) a class of equations with double singularity,
the critical Hardy-Sobolev exponent and a concave term and (III) a class of
equations in divergent form, which involves a singular term, a Leray-Lions
operator, and a function defined on Lorentz spaces.
The nonlinearities considered in problems (I) and (II), bring additional difficulties
which, as the strong singularity at zero (so blow-up may occur) and the lack of
compactness due to the presence of a Sobolev critical exponent (problem (I))
and a Hardy-Sobolev critical exponent (problem (II)). In problem (III), the
singularity implies that the standard definition of weak solution may not make
sense. Therefore is necessary to introduce a special notion of weak solution on
open subsets of the domain.
Variational methods and Critical Point Theory techniques are used to prove the
existence of solutions in the two first problems. In problem (I), our method
combines Nehari's techniques, Ekeland's variational principle, minimax
methods, a translation argument and integral estimates of the energy level. In
this case, we prove the existence of (at least) four nontrivial solutions where at
least one of them is sign-changing. In problem (II), we prove the existence of at
least two positive solutions and a pair of sign-changing solutions, using the
concentration-compactness method and the mountain pass theorem. The
approach in problem (III) combines a surjectivity result for monotone, coercive
and radially continuous operators with special properties of Leray-Lions
operators. We prove the existence of at least one solution in a Lorentz space
and obtain an estimative for the solution
On the boundedness of the Hardy operator in the weighted space BMO
No full textThe result of Golubov [5, Theorem 2] on the boundedness of the Hardy-Littlewood operator Bf(x) := 1/x integral(x)(0)f(x)dt in the space BMO(R) is well known. The author of the present paper solves the analogous problem in the weighted space BMO on the semi-axis R(+) for the operator T(w)f(x) := 1/W(x) integral(x)(0)f(t)w(t)dt, and also in the classical space BMO(R(+)) for a class of integral operators involving, for example, the Riemann-Liouville fractional integral
On the boundedness of the Hardy operator in the weighted space BMO
No full textThe result of Golubov [5, Theorem 2] on the boundedness of the Hardy-Littlewood operator Bf(x) := 1/x integral(x)(0)f(x)dt in the space BMO(R) is well known. The author of the present paper solves the analogous problem in the weighted space BMO on the semi-axis R(+) for the operator T(w)f(x) := 1/W(x) integral(x)(0)f(t)w(t)dt, and also in the classical space BMO(R(+)) for a class of integral operators involving, for example, the Riemann-Liouville fractional integral
Estimates for the norms of integral and discrete operators of Hardy type on cones of quasimonotone functions
No full textThe author claims a number of results concerning boundedness of Hardy-type operators such as (int_{0}^{t}fsp r,dmu)^{1/r} or (int_{t}^{infty}fsp r,dmu)^{1/r}, t>0, in quite a general setting on cones of functions with certain monotonicity properties; namely, the cones Omega_k of functions fgeq0 such that f/k is decreasing and Omega^{m} of functions fgeq0 such that f/m is increasing, where k,m are fixed functions on (0,infty). The results generalize earlier work of the author. Discrete versions are treated, too. Proofs are not included
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