Annals of Functional Analysis最新文献

Although a Fractional Picone’s inequality is already known for problems dealing with fractional p-Laplacian, one of its consequences is missing, the one usually used to prove the nonexistence of solutions. In this paper, we prove this result (see Theorem 1.2) and, as a consequence, we deal with a fractional p-Laplacian problem with Dirichlet boundary conditions and a nonlinearity involving a supercritical exponential term. We also study the asymptotic behavior of its solutions as (prightarrow 1^+) and (prightarrow infty), which are related to the Cheeger constant and the distance function, respectively.

In this paper, we establish a necessary and sufficient condition for two Toeplitz operators with harmonic polynomial symbols to commute on the Newton space. This condition is similar to the theorem proved by Brown–Halmos for Toeplitz operators on the Hardy space, and is also analogous to the result obtained by Axler–Čučković for Toeplitz operators with harmonic symbols on the Bergman space.

In this paper, we study the following magnetic Schrödinger operator in (mathbb {R}^3):

where (tilde{V}) is non-negative potential supported over the tube built along a curve which is a local deformation of a straight one, and (B:=textrm{curl}(A)) is a non-zero and local (i.e., a compact supported) magnetic field. We prove that the magnetic field does not alter the essential spectrum of this system and establish a sufficient condition for the discrete spectrum to be empty.

In this paper, (L^p(mathbb {R}^d,gamma _infty ))-boundedness properties for Littlewood–Paley g-functions involving time and spatial derivatives of Ornstein–Uhlenbeck semigroups are established. Here, (gamma _infty) denotes the invariant measure. To prove the strong type results for (1<p< {infty}), we use R-boundedness. The weak type (1,1) property is established by studying separately global and local operators defined for the Littlewood–Paley g-functions. By the way (L^p(mathbb {R}^d,gamma _infty ))-boundedness properties for maximal and variation operators for Ornstein–Uhlenbeck semigroups are proved.

We study (strong) first countability of locally solid convergence structures on Archimedean vector lattices. Among other results, we characterise those vector lattices for which relatively uniform-, order-, and (sigma)-order convergence, respectively, is (strongly) first countable. The implications for the validity of sequential arguments in the contexts of these convergence structures are pointed out.

This paper investigates the asymptotic behavior of fractional resolvent families in Banach spaces. We establish new results on operator equivalence under asymptotic approximation conditions, develop stability criteria for resolvent families, and extend Datko’s theorem to the fractional setting. The main technical tools include spectral theory, Laplace transform methods, and refined estimates of Mittag-Leffler functions.

We show that there exists a ground state solution for a generalized Kadomtsev–Petviashvili equation in (mathbb {R}^2). We prove that the ground state solution has energy equal to the mountain pass level of the functional corresponding to the equation.

We introduce the q-tensor product of semi-closed operators. Related basic properties between algebraic tensor products, tensor products and q-tensor products are studied. The q-tensor product of semi-closed or closed projections is considered. It is shown that the tensor product can be defined for ‘non-densely defined’ closable operators using properties of q-tensor products. As applications, we investigate relations between (q-) tensor products and the Krein—von Neumann extension of a semi-closed positive symmetric operator with the positively closable condition.

Inspired by Bohr’s equivalence relation concerning general Dirichlet series, in this paper we introduce a new equivalence relation on certain classes of exponential polynomials whose sets of frequencies are not necessarily equal. We first characterize this equivalence relation through a new perspective, and finally we obtain an improvement of Bohr’s equivalence theorem for the case of these finite exponential sums.

We introduce classes of bilinear operators of (ell _{p,q})-type, i.e. classes of operators in which their sequences of s-numbers are in (ell _{p,q},) and their properties and relationships are studied. We also introduce two classes of summing bilinear operators: the class (Pi _{p,q;r}^{ss}) of strongly summing operators, and the class (Pi _{p,q;r,s}^{as}) of absolutely summing operators. These classes share some properties with similar proofs. But, some others properties are specific for one or the other class. Also, they are somewhat more general than the multilinear summing classes introduced before by several authors. Relationships between classes of (ell _{p,q})-type and summing classes are given.