Weighted power mean discrete dynamical systems: fast convergence properties.
Weighted rearrangements and higher integrability results
Weighted Rellich inequality on -type groups and nonisotropic Heisenberg groups.
Weighted Sobolev-Lieb-Thirring inequalities.
We give a weighted version of the Sobolev-Lieb-Thirring inequality for suborthonormal functions. In the proof of our result we use phi-transform of Frazier-Jawerth.
Weighted Theorems on Fractional Integrals in the Generalized Hölder Spaces via Indices mω and Mω
Mathematics Subject Classification: 26A16, 26A33, 46E15.There are known various statements on weighted action of one-dimensional and multidimensional fractional integration operators in spaces of continuous functions, such as weighted generalized Hölder spaces Hω0(ρ) of functions with a given dominant ω of their continuity modulus.
Weighted weak type Hardy inequalities with applications to Hilbert transforms and maximal functions
Weighted weak type inequalities for the Hardy operator when .
Weighted weak-type inequalities for generalized Hardy operators.
Well behaved asymptotical convex functions
Well-Posedness of Diffusion-Wave Problem with Arbitrary Finite Number of Time Fractional Derivatives in Sobolev Spaces H^s
Mathematics Subject Classification 2010: 26A33, 33E12, 35S10, 45K05.We give the proofs of the existence and regularity of the solutions in the space C^∞ (t > 0;H^(s+2) (R^n)) ∩ C^0(t ≧ 0;H^s(R^n)); s ∊ R, for the 1-term, 2-term,..., n-term time-fractional equation evaluated from the time fractional equation of distributed order with spatial Laplace operator Δx ...
Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations
Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12In the present paper the Cauchy problem for partial inhomogeneous pseudo-differential equations of fractional order is analyzed. The solvability theorem for the Cauchy problem in the space ΨG,2(R^n) of functions in L2(R^n) whose Fourier transforms are compactly supported in a domain G ⊆ R^n is proved. The representation of the solution in terms of pseudo-differential operators is given. The solvability theorem in the Sobolev...
Werte zwischen dem geometrischen und dem arithmetischen Mittel zweier Zahlen.
When finely continuous functions are of the first class of Baire
When is any continuous function Lipschitzian?
When Lagrangean and quasi-arithmetic means coincide.
Where are typical functions one-to-one?
Suppose is closed. Is it true that the typical (in the sense of Baire category) function in is one-to-one on ? If we show that the answer to this question is yes, though we construct an with for which the answer is no. If is the middle- Cantor set we prove that the answer is yes if and only if There are ’s with Hausdorff dimension one for which the answer is still yes. Some other related results are also presented.
Whitney arcs and 1-critical arcs
A simple arc γ ⊂ ℝⁿ is called a Whitney arc if there exists a non-constant real function f on γ such that for every x ∈ γ; γ is 1-critical if there exists an f ∈ C¹(ℝⁿ) such that f’(x) = 0 for every x ∈ γ and f is not constant on γ. We show that the two notions are equivalent if γ is a quasiarc, but for general simple arcs the Whitney property is weaker. Our example also gives an arc γ in ℝ² each of whose subarcs is a monotone Whitney arc, but which is not a strictly monotone Whitney arc. This...
Whitney covers and quasi-isometry of -averaging domains.
Whitney type inequality, pointwise version
The main result of the paper estimates the asymptotic behavior of local polynomial approximation for functions at a point via the behavior of μ-differences, a generalization of the kth difference. The result is applied to prove several new and extend classical results on pointwise differentiability of functions including Marcinkiewicz-Zygmund’s and M. Weiss’ theorems. In particular, we present a solution of the problem posed in the 30s by Marcinkiewicz and Zygmund.
Whitney's extension theorem for nonquasianalytic classes of ultradifferentiable functions