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Weighted estimates for commutators of linear operators

Josefina Alvarez, Richard Bagby, Douglas Kurtz, Carlos Pérez (1993)

Studia Mathematica

We study boundedness properties of commutators of general linear operators with real-valued BMO functions on weighted L p spaces. We then derive applications to particular important operators, such as Calderón-Zygmund type operators, pseudo-differential operators, multipliers, rough singular integrals and maximal type operators.

Well-posedness for density-dependent incompressible fluids with non-Lipschitz velocity

Boris Haspot (2012)

Annales de l’institut Fourier

This paper is dedicated to the study of the initial value problem for density dependent incompressible viscous fluids in ℝ N with N ≥ 2 . We address the question of well-posedness for large and small initial data having critical Besov regularity in functional spaces as close as possible to the ones imposed in the incompressible Navier Stokes system by Cannone, Meyer and Planchon (where u 0 ∈ B p , r N p - 1 with 1 ≤ p < + ∞ , 1 ≤ r ≤ + ∞ ). This improves the classical analysis where u 0 is considered belonging in B p , 1 N p - 1 such that the velocity u remains...

Well-Posedness of Diffusion-Wave Problem with Arbitrary Finite Number of Time Fractional Derivatives in Sobolev Spaces H^s

Stojanović, Mirjana (2010)

Fractional Calculus and Applied Analysis

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

Saydamatov, Erkin (2006)

Fractional Calculus and Applied Analysis

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...

Weyl product algebras and classical modulation spaces

Anders Holst, Joachim Toft, Patrik Wahlberg (2010)

Banach Center Publications

We discuss continuity properties of the Weyl product when acting on classical modulation spaces. In particular, we prove that M p , q is an algebra under the Weyl product when p ∈ [1,∞] and 1 ≤ q ≤ min(p,p’).

When is a pseudo-differential equation solvable ?

Nicolas Lerner (2000)

Annales de l'institut Fourier

This paper begins with a broad survey of the state of the art in matters of solvability for differential and pseudo-differential equations. Then we proceed with a Hilbertian lemma which we use to prove a new solvability result.

Ψ-pseudodifferential operators and estimates for maximal oscillatory integrals

Carlos E. Kenig, Wolfgang Staubach (2007)

Studia Mathematica

We define a class of pseudodifferential operators with symbols a(x,ξ) without any regularity assumptions in the x variable and explore their L p boundedness properties. The results are applied to obtain estimates for certain maximal operators associated with oscillatory singular integrals.

Currently displaying 541 – 560 of 624