We use induction and interpolation techniques to prove that a composition operator induced by a map φ is bounded on the weighted Bergman space Aα(H) of the right half-plane if and only if φ fixes ∞ non-tangentially, and has a finite angular derivative λ there. We further prove that in this case the norm, essential norm, and spectral radius of the operator are all equal, and given by λ.

We study interior Lp-regularity theory, also known as Calderon-Zygmund of the equation〈Lsu,φ〉:=∫Rn∫RnK(x,y)(u(x)−u(y))(φ(x)−φ(y))|x−y|n+2sdxdy=〈f,φ〉,∀φ∈Cc∞(Rn). prove that for s∈(0,1), t∈[s,2s], p∈[2,∞), K an elliptic, symmetric, and K(⋅,y) is uniformly Hölder continuous, solution u belongs to Hloc2s−t,p(Ω) long 2s−t<1 f∈(H00t,p′(Ω))⁎. The increase in differentiability integrability independent...

We introduce new subclasses S σ,s k λ, δ, φ and K σ,s k λ, δ, φ of analytic functions with respect to k-symmetric points defined by differential operator. Some interesting properties for these classes are obtained.

Sufficient (almost necessary) conditions are given on the weight functions u(·), v(·) for Φ−1 2 [ ∫ Rn Φ2 ( C2(Msf)(x) ) u(x)dx ] ≤ Φ−1 1 [ C1 ∫ Rn Φ1(|f(x)|)v(x)dx ] to hold when Φ1, Φ2 are φ-functions with subadditive Φ1Φ 2 , and Ms (0 ≤ s < n), is the usual fractional maximal operator. §

This work concerns the multi-point nonlinear Neumann boundaryvalue problem involving a p-Laplacian-like operator (φ(u′))′ = f(t, u, u′), t ∈ (0, 1), u′(0) = u′(η), φ(u′(1)) = m X

This report studies an abstract approach to modeling the motion of large eddies in a turbulent flow. If the Navier-Stokes equations (NSE) are averaged with a local, spatial convolution type filter, φ = gδ ∗ φ, the resulting system is not closed due to the filtered nonlinear term uu. An approximate deconvolution operator D is a bounded linear operator which is an approximate filter inverse D(u) ...

We consider a closed set S ⊆ Rn and a linear operator Φ: R[X1, . . . , Xn]→ R[X1, . . . , Xn] that preserves nonnegative polynomials, in the following sense: if f ≥ 0 on S, then Φ(f) ≥ 0 on S as well. We show that each such operator is given by integration with respect to a measure taking nonnegative functions as its values. This can be seen as a generalization of Haviland’s Theorem, which conc...

Let φ and ψ be holomorphic maps on such that φ( ) ⊂ . Let Cφ,Mψ and D be the composition, multiplication and differentiation operators, respectively. In this paper, we consider linear operators induced by products of these operators from Bergman-Nevanlinna spaces AβN to Bloch-type spaces. In fact, we prove that these operators map AβN compactly into Bloch-type spaces if and only if they map A β...

Abstract. Let A and B be almost commuting (i.e., the commutator AB−BA belongs to trace class) self-adjoint operators. We construct a functional calculus φ 7→ φ(A,B) for functions φ in the Besov class B ∞,1(R ). This functional calculus is linear, the operators φ(A,B) and ψ(A,B) almost commute for φ, ψ ∈ B ∞,1(R ), and φ(A,B) = u(A)v(B) whenever φ(s, t) = u(s)v(t). We extend the Helton–Howe trac...