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The notion of $p$-ellipticity has recently played a significant role in improving our understanding of issues of solvability of boundary value problems for scalar complex valued elliptic PDEs. In particular, the presence of $p$-ellipticity…

In the sequel, we recall and comment some classical results on the non-increasing rearrangement and Lorentz spaces. There are papers in the existing literature that seemed to have been bypassed as regards its contractive property in~$L^p$…

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We present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of…

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There are several extensions of the classical Banach Fixed Point Theorem in technical literature. A branch of generalizations replaces usual contractivity by weaker but still effective assumptions. Our note follows this stream, presenting…

The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well known contraction…

We consider a nonlinear counterpart of a compactness lemma of J. Simon, which arises naturally in the study of doubly nonlinear equations of elliptic-parabolic type. Our work was motivated by previous results J. Simon, recently sharpened by…

Lutwak, Yang and Zhang \cite{LYZ2018} introduced the $L_p$ dual curvature measure that unifies several other geometric measures in dual Brunn-Minkowski theory and Brunn- Minkowski theory. Motivated by works in \cite{LYZ2018}, we consider…

We introduce new classes of general monotone sequences and study their properties. For functions whose Fourier coefficients belong to these classes, we establish Hardy-Littlewood-type theorems.

We extend the classical Kolmogorov-Riesz compactness theorem to the setting of asymptotic $L_p$ spaces on $\mathbb{R}^n$. These are nonlocally convex $\mathrm{F}$-spaces that contain the standard $L_p$ spaces as dense subspaces and include…

In the case (4/3)<p<4, and assuming a pair of locally finite positive Borel measures on the real line have no common point masses, we prove variants of two conjectures of T. Hyt\"onen and E. Vuorinen from 2018 on two weight testing theorems…