Search results for "Mathematics::Functional Analysis"
showing 10 items of 236 documents
Hardy-Orlicz Spaces of conformal densities
2014
We define and prove characterizations of Hardy-Orlicz spaces of conformal densities.
Some representation theorems for sesquilinear forms
2016
The possibility of getting a Radon-Nikodym type theorem and a Lebesgue-like decomposition for a non necessarily positive sesquilinear $\Omega$ form defined on a vector space $\mathcal D$, with respect to a given positive form $\Theta$ defined on $\D$, is explored. The main result consists in showing that a sesquilinear form $\Omega$ is $\Theta$-regular, in the sense that it has a Radon-Nikodym type representation, if and only if it satisfies a sort Cauchy-Schwarz inequality whose right hand side is implemented by a positive sesquilinear form which is $\Theta$-absolutely continuous. In the particular case where $\Theta$ is an inner product in $\mathcal D$, this class of sesquilinear form cov…
Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces
2015
Submitted by Alexandre Almeida (jaralmeida@ua.pt) on 2015-11-12T11:41:07Z No. of bitstreams: 1 RieszWolff_RIA.pdf: 159825 bytes, checksum: d99abdf3c874f47195619a31ff5c12c7 (MD5) Approved for entry into archive by Bella Nolasco(bellanolasco@ua.pt) on 2015-11-17T12:18:41Z (GMT) No. of bitstreams: 1 RieszWolff_RIA.pdf: 159825 bytes, checksum: d99abdf3c874f47195619a31ff5c12c7 (MD5) Made available in DSpace on 2015-11-17T12:18:41Z (GMT). No. of bitstreams: 1 RieszWolff_RIA.pdf: 159825 bytes, checksum: d99abdf3c874f47195619a31ff5c12c7 (MD5) Previous issue date: 2015-04
The “Maslov Anomaly” for the Harmonic Oscillator
2001
Specializing the discussion of the previous section to the harmonic oscillator we have for \(N = 1,\ \eta ^{a} = (p,x),\ a = 1,2,\ \eta ^{1} \equiv p,\ \eta ^{2} \equiv x\) $$\displaystyle{ H(p,x) = \frac{1} {2}\eta ^{a}\eta ^{a} = \frac{1} {2}{\bigl (p^{2} + x^{2}\bigr )}\;. }$$ (30.1) The only conserved quantity is J = H. In the action we need the combination $$\displaystyle{ \frac{1} {2}\eta ^{a}\omega _{ ab}\dot{\eta }^{b} -\mathcal{H}(\eta ) = \frac{1} {2}\eta ^{a}\left [\omega _{ ab} \frac{d} {dt} -{\bigl ( 1 + A(t)\bigr )}\mathrm{1l}_{ab}\right ]\eta ^{b} }$$ (30.2) and $$\displaystyle{ \tilde{M}_{\phantom{a}b}^{a} =\omega ^{ac}\partial _{ c}\partial _{b}(H + AJ\,) ={\bigl ( 1 + A(t)…
Algebrability of the set of hypercyclic vectors for backward shift operators
2020
Abstract We study the existence of algebras of hypercyclic vectors for weighted backward shifts on Frechet sequence spaces that are algebras when endowed with coordinatewise multiplication or with the Cauchy product. As a particular case, we obtain that the sets of hypercyclic vectors for Rolewicz's and MacLane's operators are algebrable.
Maximal potentials, maximal singular integrals, and the spherical maximal function
2014
We introduce a notion of maximal potentials and we prove that they form bounded operators from L to the homogeneous Sobolev space Ẇ 1,p for all n/(n − 1) < p < n. We apply this result to the problem of boundedness of the spherical maximal operator in Sobolev spaces.
Regularity of the Inverse of a Sobolev Homeomorphism
2011
We give necessary and sufficient conditions for the inverse ofa Sobolev homeomorphism to be a Sobolev homeomorphism and conditions under which the inverse is of bounded variation.
Generalized dimension estimates for images of porous sets under monotone Sobolev mappings
2014
We give an essentially sharp estimate in terms of generalized Hausdorff measures for images of porous sets under monotone Sobolev mappings, satisfying suitable Orlicz-Sobolev conditions.
Continuity of the maximal operator in Sobolev spaces
2006
We establish the continuity of the Hardy-Littlewood maximal operator on Sobolev spaces W 1,p (R n ), 1 < p < ∞. As an auxiliary tool we prove an explicit formula for the derivative of the maximal function.
REGULARITY OF THE FRACTIONAL MAXIMAL FUNCTION
2003
The purpose of this work is to show that the fractional maximal operator has somewhat unexpected regularity properties. The main result shows that the fractional maximal operator maps -spaces boundedly into certain first-order Sobolev spaces. It is also proved that the fractional maximal operator preserves first-order Sobolev spaces. This extends known results for the Hardy–Littlewood maximal operator.