Related papers: An inequality type condition for quasinearly subha…
In a previous paper, the author proved the existence of extremal function for the Moser-Trudinger inequality on a compact manifold. In the this paper, we will give a new proof of one of the key proposition.
In this paper, we prove several sharp Bohr-type and Bohr-Rogosinski-type inequalities for $K$-quasiconformal, sense-preserving harmonic mappings on $\mathbb{D}$, whose analytic part is subordinate to a function belonging to the class of…
We first study subextensions of m-subharmonic functions in weighted energy classes with given boundary values. The results are used to approximate an m-subharmonic function in weighted energy classes with given boundary values by an…
We prove some results which give sufficient conditions so that pointwise approximation of negative plurisubharmonic functions on complex varieties by continuous plurisubharmonic ones is possible.
In this note we show that a recent existence result on quasiequilibrium problems, which seems to improve deeply some well-known results, is not correct. We exhibit a counterexample and we furnish a generalization of a lemma about continuous…
We show that, under certain geometric conditions, there are no nonconstant quasiminimizers with finite $p$th power energy in a (not necessarily complete) metric measure space equipped with a globally doubling measure supporting a global…
We show that the Harnack inequality for a class of degenerate parabolic quasilinear PDE $$\p_t u=-X_i^* A_i(x,t,u,Xu)+ B(x,t,u,Xu),$$ associated to a system of Lipschitz continuous vector fields $X=(X_1,...,X_m)$ in in $\Om\times (0,T)$…
In this paper, we give a new generalization of the Bohr inequality in refined form both for bounded analytic functions, and for sense-preserving harmonic functions with analytic part being bounded.
The primary objective of this paper is to establish several sharp versions of improved Bohr inequalities, refined Bohr inequalities, and Bohr-Rogosinski inequalities for the class of $K$-quasiconformal sense-preserving harmonic mappings…
We construct majorants and minorants of a Gaussian function in Euclidean space that have Fourier transforms supported in a box. The majorants that we construct are shown to be extremal and our minorants are shown to be asymptotically…
We investigate existence and uniqueness of maximal plurisubharmonic functions on bounded domains with boundary data that are not assumed to be continuous or bounded. The result is applied to approximate (possibly unbounded from above)…
A result of Chernoff gives sufficient condition for an $L^2$-function on $\R^n$ to be quasi-analytic. This is a generalization of the classical Denjoy-Carleman theorem on $\R$ and of the subsequent work on $\R^n$ by Bochner and Taylor. In…
We devise variants of classical nonconforming methods for symmetric elliptic problems. These variants differ from the original ones only by transforming discrete test functions into conforming functions before applying the load functional.…
We prove concentration inequalities for functions of independent random variables {under} sub-gaussian and sub-exponential conditions. The utility of the inequalities is demonstrated by an extension of the now classical method of Rademacher…
We study the class of functions on Lipschitz-graph domains satisfying a differential-oscillation condition and show that such functions are $\epsilon$-approximable. As a consequence we obtain the quantitative Fatou theorem in the spirit of…
In this paper, approximate lower and upper Hermite--Hadamard type inequalities are obtained for functions that are approximately convex with respect to a given Chebyshev system.
We give several characterizations of parabolic (quasisuper)- minimizers in a metric measure space equipped with a doubling measure and supporting a Poincar\'e inequality. We also prove a version of comparison principle for super- and…
We establish the full range of the Caffarelli-Kohn-Nirenberg inequalities for radial functions in the Sobolev and the fractional Sobolev spaces of order $0 < s \le 1$. In particular, we show that the range of the parameters for radial…
We give a local characterization of the class of functions having positive distributional derivative with respect to $\bar{z}$ that are almost everywhere equal to one of finitely many analytic functions and satisfy some mild non-degeneracy…
We introduce the notion of quasimonotone polar of a multivalued operator, in a similar way as the well-known monotone polar due to Martinez-Legaz and Svaiter. We first recover several properties similar to the monotone polar, including a…