Under mild conditions on the weight function K we characterize lacunary series in QK(p,q) spaces, where QK(p,q) spaces are QK type spaces of functions analytic in the unit disk.

In this paper, we investigate the generalized Hyers– Ulam– Rassias stability of the functional equation ∑i=1mf(mxi

Inner functions in QK(p,q) are studied, provided K satisfies certain regularity conditions. In particular, it is shown that the only inner functions in QK(p, p-2), p≥1, are precisely the Blaschke products whose zeros {zn} satisfy supa∈D∑K(1-|φa(zn)|2)<∞.

A Schrödinger equation and system with magnetic fields and Hardy-Sobolev critical exponents are investigated in this paper, and, under proper conditions, the existence of ground state solutions to these two problems is given.

We develop a transference method to obtain the -continuity of the Gaussian-Littlewood-Paley -function and the -continuity of the Laguerre-Littlewood-Paley -function from the -continuity of the Jacobi-Littlewood-Paley -function, in dimension one, using the well-known asymptotic relations between Jacobi polynomials and Hermite and Laguerre polynomials.

We study the sufficient conditions for the existence of a unique common fixed point of generalized --Geraghty contractions in an -complete partial -metric space. We give an example in support of our findings. Our work generalizes many existing results in the literature. As an application of our findings we demonstrate the existence of the solution of the system of elliptic...

We will prove the generalized Hyers-Ulam stability of the (inhomogeneous) diffusion equation with a source, , for a class of scalar functions with continuous second partial derivatives.

Some new coupled coincidence point and coupled fixed point theorems are established in partially ordered metric-like spaces, which generalize many results in corresponding literatures. An example is given to support our main results. As an application, we discuss the existence of the solutions for a class of nonlinear integral equations.

We give derivative and Lipschitz type characterizations of Bergman spaces with log-Hölder continuous variable exponent.

We show that the sufficient condition of the above mentioned paper is also necessary for the boundedness of Bergman type projections on a class of regulated domains.

In this paper, we study the Strang-Fix theory for approximation order in the weighted Lp -spaces and Herz spaces.

A codomain for a nonzero constant-coefficient linear partial differential operator P(∂) with fundamental solution E is a space of distributions T for which it is possible to define the convolution E*T and thus solving the equation P(∂)S=T. We identify codomains for the Cauchy-Riemann operator in ℝ2 and Laplace operator in ℝ2 . The convolution is understood in the sense of the S...

An asymptotic formula for the essential norm of the composition operator Cφ(f):=f∘φ, induced by an analytic self-map φ of the unit disc, mapping from the α-Bloch space ℬα or the Dirichlet type space Dαp into Qk(p,q) is established in terms of an integral condition.

Under mild conditions on the weight function K we characterize lacunary series in QK(p,q) spaces, where QK(p,q) spaces are QK type spaces of functions analytic in the unit disk.

In this paper we study the set of ℊ-valued functions which can be approximated by ℊ-valued continuous functions in the norm Lℊ∞(I,w), where I⊂ℝ is a compact interval, ℊ is a separable real Hilbert space and w is a certain ℊ-valued weakly measurable weight. Thus, we obtain a new extension of the celebrated Weierstrass approximation theorem.

We study a new trace problem for functions holomorphic on polyballs which generalize a known diagonal map problem for polydisk. Also, we give descriptions of traces for several concrete functional classes on polyballs defined with the help of area operator or Bergman metric ball.

This work is an introduction of weighted Besov spaces of holomorphic functions on the polydisk. Let Un be the unit polydisk in Cn and S be the space of functions of regular variation. Let 1≤p<∞,ω=(ω1,…,ωn),ωj∈S(1≤j≤n) and f∈H(Un). The function f is said to be an element of the holomorphic Besov space Bp(ω) if ‖f‖Bp(ω)p=∫Un|Df(z)|p∏j=1nωj(1-|zj|)/(1-|zj|2)2-pdm2n(z)<

We prove a homogenization result for monotone operators by using the method of multiscale convergence. More precisely, we study the asymptotic behavior as ε→0 of the solutions uε of the nonlinear equation divaε(x,∇uε)=divbε, where both aε and bε oscillate rapidly on several microscopic scales and aε satisfies certain continuity, monotonicity and boundedness conditions. This...

We consider the following fractional p-Laplacian equation: , where , , , is the fractional -Laplacian, and and for a.e. . has the subcritical growth but higher than ; however, the nonlinearity may change sign. If is coercive, we investigate the existence of ground state solutions for p-Laplacian equation.

We consider the following fractional p-Laplacian equation: , where , , , is the fractional -Laplacian, and and for a.e. . has the subcritical growth but higher than ; however, the nonlinearity may change sign. If is coercive, we investigate the existence of ground state solutions for p-Laplacian equation.

Using the fixed point index, we establish two existence theorems for positive solutions to a system of semipositone fractional difference boundary value problems. We adopt nonnegative concave functions and nonnegative matrices to characterize the coupling behavior of our nonlinear terms.

We consider the robust asymptotical stabilization of uncertain a class of descriptor fractional-order systems. In the state matrix, we require that the parameter uncertainties are time-invariant and norm-bounded. We derive a sufficient condition for the system with the fractional-order satisfying in terms of linear matrix inequalities (LMIs). The condition of the proposed...

We generalize results concerning averaged controllability on fractional type equations: system of fractional ODEs and the fractional diffusion equation. The proofs are accomplished by introducing appropriate Banach space in which we prove observability inequalities.

Suppose is a nonnegative, self-adjoint differential operator. In this paper, we introduce the Herz-type Hardy spaces associated with operator . Then, similar to the atomic and molecular decompositions of classical Herz-type Hardy spaces and the Hardy space associated with operators, we prove the atomic and molecular decompositions of the Herz-type Hardy spaces associated with...