Dang Tuan - Academia.edu (original) (raw)

Papers by Dang Tuan

Research paper thumbnail of IOSEVICH'S PROOF OF THE FALCONER THEOREM

Iosevich used the Stein-Tomas restriction theorem to give an alternative proof of a result due to... more Iosevich used the Stein-Tomas restriction theorem to give an alternative proof of a result due to Falconer which says that if the Hausdor dimension of a subset of Rd; d  2; is greater than (d + 1)=2, then the Lebesgue measure of the set of distances is positive. In this note I give some more detailed arguments supporting to Iosevich's proof.

Research paper thumbnail of A SHORT PROOF OF THE CONVERSE TO A THEOREM OF STEINHAUS

A result of H. Steinhaus states that any positive Lebesgue measurable set has a property that its... more A result of H. Steinhaus states that any positive Lebesgue measurable set has a property that its di erence set contains an open interval around the origin. Y. V. Mospan proved that this result is the characterization of absolutely continuous measure. In this note we give a short proof of it.

Research paper thumbnail of Semilinear boundary value problems for degenerate pseudodifferential operators in spaces of Sobolev type

Russian Journal of Mathematical Physics, 2008

Boundary value problems for degenerate semilinear elliptic pseudodifferential operators are consi... more Boundary value problems for degenerate semilinear elliptic pseudodifferential operators are considered. Using the apparatus of the theory of pseudodifferential operators, function spaces introduced in [4 8], and the Rabinowitz construction [12] based on the Borsuk theorem (see [11]), we prove the existence of solutions of the problem in suitable function spaces.

Research paper thumbnail of Nonclassical semilinear boundary value problem for parabolic pseudodifferential equations in Sobolev spaces

Doklady Mathematics, 2006

Research paper thumbnail of Semilinear boundary value problems for degenerate pseudodifferential operators in spaces of Sobolev type

Russian Journal of Mathematical Physics, 2008

Boundary value problems for degenerate semilinear elliptic pseudodifferential operators are consi... more Boundary value problems for degenerate semilinear elliptic pseudodifferential operators are considered. Using the apparatus of the theory of pseudodifferential operators, function spaces introduced in [4–8], and the Rabinowitz construction [12] based on the Borsuk theorem (see [11]), we prove the existence of solutions of the problem in suitable function spaces.

Research paper thumbnail of On a semilinear boundary value problem for degenerate parabolic pseudodifferential equations

Doklady Mathematics, 2009

Research paper thumbnail of On a semilinear degenerate elliptic boundary value problem for pseudodifferential equations

Doklady Mathematics, 2009

Research paper thumbnail of A semilinear non-classical pseudodifferential boundary value problem in the Sobolev spaces

Comptes Rendus Mathematique, 2003

We study the solvability of a semilinear non-classical pseudodifferential boundary value problem ... more We study the solvability of a semilinear non-classical pseudodifferential boundary value problem in the Sobolev spaces H l,p,q , 1 < p < ∞, depending on a complex parameter q. To cite this article: Y.V. Egorov et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).

Research paper thumbnail of Semilinear boundary value problems for degenerate pseudodifferential operators in spaces of Sobolev type

Russian Journal of Mathematical Physics, 2008

Boundary value problems for degenerate semilinear elliptic pseudodifferential operators are consi... more Boundary value problems for degenerate semilinear elliptic pseudodifferential operators are considered. Using the apparatus of the theory of pseudodifferential operators, function spaces introduced in [4 8], and the Rabinowitz construction [12] based on the Borsuk theorem (see [11]), we prove the existence of solutions of the problem in suitable function spaces.

Research paper thumbnail of Nonclassical semilinear boundary value problem for parabolic pseudodifferential equations in Sobolev spaces

Doklady Mathematics, 2006

Research paper thumbnail of Semilinear boundary value problems for degenerate pseudodifferential operators in spaces of Sobolev type

Russian Journal of Mathematical Physics, 2008

Boundary value problems for degenerate semilinear elliptic pseudodifferential operators are consi... more Boundary value problems for degenerate semilinear elliptic pseudodifferential operators are considered. Using the apparatus of the theory of pseudodifferential operators, function spaces introduced in [4–8], and the Rabinowitz construction [12] based on the Borsuk theorem (see [11]), we prove the existence of solutions of the problem in suitable function spaces.

Research paper thumbnail of On a semilinear boundary value problem for degenerate parabolic pseudodifferential equations

Doklady Mathematics, 2009

Research paper thumbnail of On a semilinear degenerate elliptic boundary value problem for pseudodifferential equations

Doklady Mathematics, 2009

Research paper thumbnail of A semilinear non-classical pseudodifferential boundary value problem in the Sobolev spaces

Comptes Rendus Mathematique, 2003

We study the solvability of a semilinear non-classical pseudodifferential boundary value problem ... more We study the solvability of a semilinear non-classical pseudodifferential boundary value problem in the Sobolev spaces H l,p,q , 1 < p < ∞, depending on a complex parameter q. To cite this article: Y.V. Egorov et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).

Research paper thumbnail of Some remarks on the paper "Some elementary inequalities" of G. Bennett

We give some counterexamples and some remarks of some of the corollaries of Bennett's paper, invo... more We give some counterexamples and some remarks of some of the corollaries of Bennett's paper, involving the weighted mean matrices on l p . We also discuss Littlewood's problem.

Research paper thumbnail of IOSEVICH'S PROOF OF THE FALCONER THEOREM

Iosevich used the Stein-Tomas restriction theorem to give an alternative proof of a result due to... more Iosevich used the Stein-Tomas restriction theorem to give an alternative proof of a result due to Falconer which says that if the Hausdor dimension of a subset of Rd; d  2; is greater than (d + 1)=2, then the Lebesgue measure of the set of distances is positive. In this note I give some more detailed arguments supporting to Iosevich's proof.

Research paper thumbnail of A SHORT PROOF OF THE CONVERSE TO A THEOREM OF STEINHAUS

A result of H. Steinhaus states that any positive Lebesgue measurable set has a property that its... more A result of H. Steinhaus states that any positive Lebesgue measurable set has a property that its di erence set contains an open interval around the origin. Y. V. Mospan proved that this result is the characterization of absolutely continuous measure. In this note we give a short proof of it.

Research paper thumbnail of Semilinear boundary value problems for degenerate pseudodifferential operators in spaces of Sobolev type

Russian Journal of Mathematical Physics, 2008

Boundary value problems for degenerate semilinear elliptic pseudodifferential operators are consi... more Boundary value problems for degenerate semilinear elliptic pseudodifferential operators are considered. Using the apparatus of the theory of pseudodifferential operators, function spaces introduced in [4 8], and the Rabinowitz construction [12] based on the Borsuk theorem (see [11]), we prove the existence of solutions of the problem in suitable function spaces.

Research paper thumbnail of Nonclassical semilinear boundary value problem for parabolic pseudodifferential equations in Sobolev spaces

Doklady Mathematics, 2006

Research paper thumbnail of Semilinear boundary value problems for degenerate pseudodifferential operators in spaces of Sobolev type

Russian Journal of Mathematical Physics, 2008

Boundary value problems for degenerate semilinear elliptic pseudodifferential operators are consi... more Boundary value problems for degenerate semilinear elliptic pseudodifferential operators are considered. Using the apparatus of the theory of pseudodifferential operators, function spaces introduced in [4–8], and the Rabinowitz construction [12] based on the Borsuk theorem (see [11]), we prove the existence of solutions of the problem in suitable function spaces.

Research paper thumbnail of On a semilinear boundary value problem for degenerate parabolic pseudodifferential equations

Doklady Mathematics, 2009

Research paper thumbnail of On a semilinear degenerate elliptic boundary value problem for pseudodifferential equations

Doklady Mathematics, 2009

Research paper thumbnail of A semilinear non-classical pseudodifferential boundary value problem in the Sobolev spaces

Comptes Rendus Mathematique, 2003

We study the solvability of a semilinear non-classical pseudodifferential boundary value problem ... more We study the solvability of a semilinear non-classical pseudodifferential boundary value problem in the Sobolev spaces H l,p,q , 1 < p < ∞, depending on a complex parameter q. To cite this article: Y.V. Egorov et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).

Research paper thumbnail of Semilinear boundary value problems for degenerate pseudodifferential operators in spaces of Sobolev type

Russian Journal of Mathematical Physics, 2008

Boundary value problems for degenerate semilinear elliptic pseudodifferential operators are consi... more Boundary value problems for degenerate semilinear elliptic pseudodifferential operators are considered. Using the apparatus of the theory of pseudodifferential operators, function spaces introduced in [4 8], and the Rabinowitz construction [12] based on the Borsuk theorem (see [11]), we prove the existence of solutions of the problem in suitable function spaces.

Research paper thumbnail of Nonclassical semilinear boundary value problem for parabolic pseudodifferential equations in Sobolev spaces

Doklady Mathematics, 2006

Research paper thumbnail of Semilinear boundary value problems for degenerate pseudodifferential operators in spaces of Sobolev type

Russian Journal of Mathematical Physics, 2008

Boundary value problems for degenerate semilinear elliptic pseudodifferential operators are consi... more Boundary value problems for degenerate semilinear elliptic pseudodifferential operators are considered. Using the apparatus of the theory of pseudodifferential operators, function spaces introduced in [4–8], and the Rabinowitz construction [12] based on the Borsuk theorem (see [11]), we prove the existence of solutions of the problem in suitable function spaces.

Research paper thumbnail of On a semilinear boundary value problem for degenerate parabolic pseudodifferential equations

Doklady Mathematics, 2009

Research paper thumbnail of On a semilinear degenerate elliptic boundary value problem for pseudodifferential equations

Doklady Mathematics, 2009

Research paper thumbnail of A semilinear non-classical pseudodifferential boundary value problem in the Sobolev spaces

Comptes Rendus Mathematique, 2003

We study the solvability of a semilinear non-classical pseudodifferential boundary value problem ... more We study the solvability of a semilinear non-classical pseudodifferential boundary value problem in the Sobolev spaces H l,p,q , 1 < p < ∞, depending on a complex parameter q. To cite this article: Y.V. Egorov et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).

Research paper thumbnail of Some remarks on the paper "Some elementary inequalities" of G. Bennett

We give some counterexamples and some remarks of some of the corollaries of Bennett's paper, invo... more We give some counterexamples and some remarks of some of the corollaries of Bennett's paper, involving the weighted mean matrices on l p . We also discuss Littlewood's problem.